201. The SI unit of heat capacity is:
ⓐ. \(\text{W m}^{-1}\text{K}^{-1}\)
ⓑ. \(\text{J K}^{-1}\)
ⓒ. \(\text{kg K}^{-1}\)
ⓓ. \(\text{J kg}^{-1}\text{K}^{-1}\)
Correct Answer: \(\text{J K}^{-1}\)
Explanation: Heat capacity is defined by \(C=\frac{Q}{\Delta T}\). Heat \(Q\) is measured in joule, \(\text{J}\). Temperature change \(\Delta T\) is measured in kelvin, \(\text{K}\). Therefore, the unit of heat capacity is \(\text{J K}^{-1}\). The unit \(\text{J kg}^{-1}\text{K}^{-1}\) belongs to specific heat capacity, which is heat capacity per unit mass. The absence of \(\text{kg}^{-1}\) in \(\text{J K}^{-1}\) shows that heat capacity refers to the whole body.
202. A body absorbs \(1500\,\text{J}\) of heat and its temperature rises by \(5\,\text{K}\). What is its heat capacity?
ⓐ. \(300\,\text{J K}^{-1}\)
ⓑ. \(7500\,\text{J K}^{-1}\)
ⓒ. \(0.0033\,\text{J K}^{-1}\)
ⓓ. \(150\,\text{J K}^{-1}\)
Correct Answer: \(300\,\text{J K}^{-1}\)
Explanation: \( \textbf{Heat supplied:} \) \(Q=1500\,\text{J}\).
\( \textbf{Temperature rise:} \) \(\Delta T=5\,\text{K}\).
Heat capacity is heat required per unit temperature rise:
\[
C=\frac{Q}{\Delta T}
\]
Substitute the values:
\[
C=\frac{1500}{5}
\]
\[
C=300\,\text{J K}^{-1}
\]
The unit is \(\text{J K}^{-1}\) because heat is divided by temperature change.
The option \(7500\,\text{J K}^{-1}\) comes from multiplying \(Q\) and \(\Delta T\), which is not the definition.
\( \textbf{Final answer:} \) The heat capacity is \(300\,\text{J K}^{-1}\).
203. Two copper blocks are at the same temperature. Block \(P\) has mass \(1\,\text{kg}\), and block \(Q\) has mass \(3\,\text{kg}\). Compared with block \(P\), the heat capacity of block \(Q\) is:
ⓐ. about three times larger
ⓑ. smaller because its temperature is the same
ⓒ. the same because both are copper
ⓓ. zero because copper is a metal
Correct Answer: about three times larger
Explanation: Heat capacity belongs to a whole body, not just to the material name. For the same substance, heat capacity is proportional to mass. Block \(Q\) has three times the mass of block \(P\). Therefore, it needs about three times as much heat for the same temperature rise. Equal initial temperature does not make their heat capacities equal. The material is the same, but the amount of material is different.
204. A graph is plotted with heat supplied \(Q\) on the vertical axis and temperature rise \(\Delta T\) on the horizontal axis for a body. If the graph is a straight line through the origin, its slope represents:
ⓐ. heat capacity \(C\)
ⓑ. temperature itself \(T\)
ⓒ. coefficient of expansion \(\alpha\)
ⓓ. reciprocal of heat capacity \(\frac{1}{C}\)
Correct Answer: heat capacity \(C\)
Explanation: Heat capacity is defined by
\[
C=\frac{Q}{\Delta T}
\]
For a graph of \(Q\) on the vertical axis against \(\Delta T\) on the horizontal axis, the slope is
\[
\frac{Q}{\Delta T}
\]
Therefore, the slope represents \(C\). A steeper graph means more heat is required for the same temperature rise, so the body has a larger heat capacity. The reciprocal \(\frac{1}{C}\) would appear as the slope if \(\Delta T\) were plotted against \(Q\). This graph interpretation directly connects experimental heating data with heat capacity.
205. A body with heat capacity \(400\,\text{J K}^{-1}\) is supplied \(2000\,\text{J}\) of heat. If there is no phase change and no heat loss, the temperature rise is:
ⓐ. \(400\,\text{K}\)
ⓑ. \(2\,\text{K}\)
ⓒ. \(800\,\text{K}\)
ⓓ. \(5\,\text{K}\)
Correct Answer: \(5\,\text{K}\)
Explanation: \( \textbf{Heat capacity:} \) \(C=400\,\text{J K}^{-1}\).
\( \textbf{Heat supplied:} \) \(Q=2000\,\text{J}\).
Use the definition:
\[
C=\frac{Q}{\Delta T}
\]
Rearrange for temperature rise:
\[
\Delta T=\frac{Q}{C}
\]
Substitute:
\[
\Delta T=\frac{2000}{400}
\]
\[
\Delta T=5\,\text{K}
\]
The condition of no phase change is important because the supplied heat is then used to raise temperature.
If a phase change were occurring, heat could be absorbed without the same temperature rise.
\( \textbf{Final answer:} \) The temperature rise is \(5\,\text{K}\).
206. Consider the following statements about heat capacity.
Statement I: Heat capacity depends on the mass of the body.
Statement II: Heat capacity has unit \(\text{J K}^{-1}\).
Statement III: Heat capacity is always a material property independent of the amount of substance.
ⓐ. Statements II and III only
ⓑ. Statements I, II, and III
ⓒ. Statements I and II only
ⓓ. Statements I and III only
Correct Answer: Statements I and II only
Explanation: Statement I is correct because a larger body of the same material generally needs more heat for the same temperature rise. Statement II is correct because heat capacity is heat per unit temperature change, so its unit is \(\text{J K}^{-1}\). Statement III is not correct because heat capacity is a property of the whole body and depends on the amount of substance present. The material-independent quantity is not heat capacity but specific heat capacity, which is defined per unit mass. This is why \(C\) and \(c\) must not be used as if they mean the same thing. The capital \(C\) usually refers to the body, while small \(c\) refers to the material per unit mass.
207. A small metal ball and a large metal ball are made of the same material. Both are to be heated through \(10\,\text{K}\). The larger ball needs more heat mainly because:
ⓐ. it has lower temperature change
ⓑ. it has greater heat capacity
ⓒ. it has no molecular motion
ⓓ. it cannot absorb heat
Correct Answer: it has greater heat capacity
Explanation: Heat capacity measures the heat needed to raise the temperature of a whole body by \(1\,\text{K}\). The larger ball contains more material, so its heat capacity is larger than that of the small ball of the same substance. For the same temperature rise, the larger heat capacity requires more heat input. The temperature rise is given as the same for both balls. The difference is not due to absence of molecular motion or inability to absorb heat. It comes from the greater amount of matter that must be warmed.
208. A heating record for a body gives the following data.
| Heat supplied \(Q\) | Temperature rise \(\Delta T\) |
|---|
| \(600\,\text{J}\) | \(3\,\text{K}\) |
| \(1000\,\text{J}\) | \(5\,\text{K}\) |
| \(1600\,\text{J}\) | \(8\,\text{K}\) |
What heat capacity is indicated by this data?
ⓐ. \(200\,\text{J K}^{-1}\)
ⓑ. \(300\,\text{J K}^{-1}\)
ⓒ. \(500\,\text{J K}^{-1}\)
ⓓ. \(100\,\text{J K}^{-1}\)
Correct Answer: \(200\,\text{J K}^{-1}\)
Explanation: Heat capacity is found from
\[
C=\frac{Q}{\Delta T}
\]
Use the first data pair:
\[
C=\frac{600}{3}=200\,\text{J K}^{-1}
\]
Check with the second data pair:
\[
C=\frac{1000}{5}=200\,\text{J K}^{-1}
\]
Check with the third data pair:
\[
C=\frac{1600}{8}=200\,\text{J K}^{-1}
\]
All three readings give the same value, so the data are consistent.
The constant ratio \(Q/\Delta T\) shows that the body’s heat capacity is \(200\,\text{J K}^{-1}\).
\( \textbf{Final answer:} \) The heat capacity is \(200\,\text{J K}^{-1}\).
209. Specific heat capacity of a substance is the heat required to raise the temperature of:
ⓐ. any body by \(1\,\text{J}\)
ⓑ. unit volume of the substance by \(1\,\text{m}\)
ⓒ. the whole body by \(1\,\text{K}\)
ⓓ. unit mass of the substance by \(1\,\text{K}\)
Correct Answer: unit mass of the substance by \(1\,\text{K}\)
Explanation: Specific heat capacity is defined for unit mass of a substance. It tells how much heat is needed to raise the temperature of \(1\,\text{kg}\) of that substance by \(1\,\text{K}\). This makes it a material property, unlike heat capacity, which belongs to a particular body. A larger mass of the same substance needs more total heat, but its specific heat capacity remains the same. The temperature interval may also be expressed as \(1^\circ\text{C}\) because \(1\,\text{K}\) and \(1^\circ\text{C}\) are equal intervals. The phrase “unit mass” is the key difference between \(c\) and \(C\).
210. The relation defining specific heat capacity \(c\) is:
ⓐ. \(c=mQ\Delta T\)
ⓑ. \(c=\frac{Q}{\Delta T}\)
ⓒ. \(c=\frac{m\Delta T}{Q}\)
ⓓ. \(c=\frac{Q}{m\Delta T}\)
Correct Answer: \(c=\frac{Q}{m\Delta T}\)
Explanation: Specific heat capacity is heat required per unit mass per unit temperature rise. If heat \(Q\) is supplied to mass \(m\) and the temperature changes by \(\Delta T\), then the heat per unit mass per unit temperature rise is \(c=\frac{Q}{m\Delta T}\). The formula \(C=\frac{Q}{\Delta T}\) gives heat capacity of the whole body, not specific heat capacity. The mass appears in the denominator because specific heat capacity is measured per kilogram. The expression also uses temperature change, not absolute temperature. This formula later rearranges to \(Q=mc\Delta T\) for heating without phase change.
211. The SI unit of specific heat capacity is:
ⓐ. \(\text{J kg}^{-1}\text{K}^{-1}\)
ⓑ. \(\text{kg J}^{-1}\text{K}^{-1}\)
ⓒ. \(\text{J K}^{-1}\)
ⓓ. \(\text{W m}^{-1}\text{K}^{-1}\)
Correct Answer: \(\text{J kg}^{-1}\text{K}^{-1}\)
Explanation: From \(c=\frac{Q}{m\Delta T}\), heat \(Q\) is measured in \(\text{J}\), mass \(m\) in \(\text{kg}\), and temperature change \(\Delta T\) in \(\text{K}\). Therefore, the unit of \(c\) is \(\text{J kg}^{-1}\text{K}^{-1}\). The unit \(\text{J K}^{-1}\) is for heat capacity \(C\), not specific heat capacity \(c\). The extra factor \(\text{kg}^{-1}\) shows that the quantity is per unit mass. The unit \(\text{W m}^{-1}\text{K}^{-1}\) belongs to thermal conductivity. Correct unit choice helps distinguish thermal quantities that otherwise look similar.
212. A \(0.50\,\text{kg}\) metal block absorbs \(900\,\text{J}\) of heat, and its temperature rises by \(30\,\text{K}\). What is its specific heat capacity?
ⓐ. \(120\,\text{J kg}^{-1}\text{K}^{-1}\)
ⓑ. \(30\,\text{J kg}^{-1}\text{K}^{-1}\)
ⓒ. \(1800\,\text{J kg}^{-1}\text{K}^{-1}\)
ⓓ. \(60\,\text{J kg}^{-1}\text{K}^{-1}\)
Correct Answer: \(60\,\text{J kg}^{-1}\text{K}^{-1}\)
Explanation: \( \textbf{Heat supplied:} \) \(Q=900\,\text{J}\).
\( \textbf{Mass of block:} \) \(m=0.50\,\text{kg}\).
\( \textbf{Temperature rise:} \) \(\Delta T=30\,\text{K}\).
Specific heat capacity is
\[
c=\frac{Q}{m\Delta T}
\]
Substitute the values:
\[
c=\frac{900}{(0.50)(30)}
\]
Calculate the denominator:
\[
(0.50)(30)=15
\]
So,
\[
c=\frac{900}{15}=60\,\text{J kg}^{-1}\text{K}^{-1}
\]
The mass must be included because \(c\) is heat per unit mass per unit temperature rise.
\( \textbf{Final answer:} \) \(c=60\,\text{J kg}^{-1}\text{K}^{-1}\).
213. Heat capacity \(C\) and specific heat capacity \(c\) are related for a body of mass \(m\) by:
ⓐ. \(C=\frac{c}{m}\)
ⓑ. \(C=mc\)
ⓒ. \(C=\frac{m}{c}\)
ⓓ. \(C=m+c\)
Correct Answer: \(C=mc\)
Explanation: Heat capacity of a body is \(C=\frac{Q}{\Delta T}\). Specific heat capacity is \(c=\frac{Q}{m\Delta T}\). Multiplying \(c\) by mass \(m\) gives
\[
mc=m\frac{Q}{m\Delta T}
\]
The mass cancels, leaving
\[
mc=\frac{Q}{\Delta T}=C
\]
Thus, \(C=mc\). This shows why heat capacity depends on the amount of substance, while specific heat capacity is a property of the material. A larger mass of the same material has larger \(C\), but the same \(c\).
214. A body has mass \(2.0\,\text{kg}\) and specific heat capacity \(450\,\text{J kg}^{-1}\text{K}^{-1}\). Its heat capacity is:
ⓐ. \(225\,\text{J K}^{-1}\)
ⓑ. \(1800\,\text{J K}^{-1}\)
ⓒ. \(450\,\text{J K}^{-1}\)
ⓓ. \(900\,\text{J K}^{-1}\)
Correct Answer: \(900\,\text{J K}^{-1}\)
Explanation: \( \textbf{Mass:} \) \(m=2.0\,\text{kg}\).
\( \textbf{Specific heat capacity:} \) \(c=450\,\text{J kg}^{-1}\text{K}^{-1}\).
Heat capacity of a body is related to specific heat capacity by
\[
C=mc
\]
Substitute the values:
\[
C=(2.0)(450)
\]
\[
C=900\,\text{J K}^{-1}
\]
The unit \(\text{kg}\) cancels with \(\text{kg}^{-1}\), leaving \(\text{J K}^{-1}\).
The result is a property of this whole \(2.0\,\text{kg}\) body, not of unit mass.
\( \textbf{Final answer:} \) \(C=900\,\text{J K}^{-1}\).
215. Two equal masses of water and copper receive the same amount of heat, and neither changes state. Water has a much larger specific heat capacity than copper. The temperature rise of water will be:
ⓐ. exactly equal to that of copper always
ⓑ. smaller than that of copper
ⓒ. zero because water cannot be heated
ⓓ. larger than that of copper
Correct Answer: smaller than that of copper
Explanation: For heating without phase change, the relation is \(Q=mc\Delta T\). If \(Q\) and \(m\) are the same for two substances, then \(\Delta T\) is inversely related to \(c\). Water has a larger specific heat capacity, so it needs more heat for each unit temperature rise. With the same heat input, its temperature rise is smaller. Copper has a smaller specific heat capacity, so the same heat produces a larger temperature rise. This is why water warms and cools more slowly than many metals.
216. A \(200\,\text{g}\) sample of a liquid requires \(4200\,\text{J}\) of heat to raise its temperature by \(10\,\text{K}\). What is its specific heat capacity?
ⓐ. \(210\,\text{J kg}^{-1}\text{K}^{-1}\)
ⓑ. \(420\,\text{J kg}^{-1}\text{K}^{-1}\)
ⓒ. \(2100\,\text{J kg}^{-1}\text{K}^{-1}\)
ⓓ. \(4200\,\text{J kg}^{-1}\text{K}^{-1}\)
Correct Answer: \(2100\,\text{J kg}^{-1}\text{K}^{-1}\)
Explanation: \( \textbf{Given heat:} \) \(Q=4200\,\text{J}\).
\( \textbf{Mass:} \) \(200\,\text{g}=0.200\,\text{kg}\).
\( \textbf{Temperature rise:} \) \(\Delta T=10\,\text{K}\).
Use the definition:
\[
c=\frac{Q}{m\Delta T}
\]
Substitute:
\[
c=\frac{4200}{(0.200)(10)}
\]
Calculate the denominator:
\[
(0.200)(10)=2.00
\]
Therefore,
\[
c=\frac{4200}{2.00}=2100\,\text{J kg}^{-1}\text{K}^{-1}
\]
The gram-to-kilogram conversion is necessary because the SI unit of \(c\) uses \(\text{kg}^{-1}\).
\( \textbf{Final answer:} \) \(c=2100\,\text{J kg}^{-1}\text{K}^{-1}\).
217. Study the table and identify the row that correctly distinguishes \(C\) and \(c\).
| Row | Quantity | Meaning | Unit |
|---|
| P | \(C\) | Heat capacity of a body | \(\text{J K}^{-1}\) |
| Q | \(c\) | Heat capacity of a whole body | \(\text{J K}^{-1}\) |
| R | \(C\) | Specific heat capacity | \(\text{J kg}^{-1}\text{K}^{-1}\) |
| S | \(c\) | Latent heat | \(\text{J kg}^{-1}\) |
ⓐ. Row S only
ⓑ. Row R only
ⓒ. Row P only
ⓓ. Row Q only
Correct Answer: Row P only
Explanation: The symbol \(C\) usually denotes heat capacity of a whole body, and its unit is \(\text{J K}^{-1}\). The symbol \(c\) denotes specific heat capacity, which is heat capacity per unit mass, with unit \(\text{J kg}^{-1}\text{K}^{-1}\). Row Q wrongly assigns the meaning and unit of heat capacity to \(c\). Row R reverses \(C\) and \(c\). Row S confuses specific heat capacity with latent heat, which is used for phase change. The table shows why the capital and small letters must be kept separate.
218. A graph of heat supplied \(Q\) against temperature rise \(\Delta T\) is drawn for \(1\,\text{kg}\) of a substance. The graph is a straight line through the origin with slope \(900\,\text{J K}^{-1}\). What is the specific heat capacity of the substance?
ⓐ. \(90\,\text{J kg}^{-1}\text{K}^{-1}\)
ⓑ. \(900\,\text{J kg}^{-1}\text{K}^{-1}\)
ⓒ. \(1800\,\text{J kg}^{-1}\text{K}^{-1}\)
ⓓ. \(450\,\text{J kg}^{-1}\text{K}^{-1}\)
Correct Answer: \(900\,\text{J kg}^{-1}\text{K}^{-1}\)
Explanation: For a graph of \(Q\) against \(\Delta T\), the slope is
\[
\frac{Q}{\Delta T}
\]
This slope represents the heat capacity \(C\) of the sample.
Given slope:
\[
C=900\,\text{J K}^{-1}
\]
The sample mass is \(1\,\text{kg}\).
Since
\[
C=mc
\]
we have
\[
c=\frac{C}{m}
\]
Substitute:
\[
c=\frac{900}{1}=900\,\text{J kg}^{-1}\text{K}^{-1}
\]
For a \(1\,\text{kg}\) sample, the numerical values of \(C\) and \(c\) are equal, but their units and meanings remain different.
\( \textbf{Final answer:} \) \(c=900\,\text{J kg}^{-1}\text{K}^{-1}\).
219. A \(0.25\,\text{kg}\) solid has heat capacity \(100\,\text{J K}^{-1}\). Its specific heat capacity is:
ⓐ. \(400\,\text{J kg}^{-1}\text{K}^{-1}\)
ⓑ. \(100\,\text{J kg}^{-1}\text{K}^{-1}\)
ⓒ. \(25\,\text{J kg}^{-1}\text{K}^{-1}\)
ⓓ. \(250\,\text{J kg}^{-1}\text{K}^{-1}\)
Correct Answer: \(400\,\text{J kg}^{-1}\text{K}^{-1}\)
Explanation: \( \textbf{Heat capacity:} \) \(C=100\,\text{J K}^{-1}\).
\( \textbf{Mass:} \) \(m=0.25\,\text{kg}\).
The relation between heat capacity and specific heat capacity is
\[
C=mc
\]
Rearrange:
\[
c=\frac{C}{m}
\]
Substitute:
\[
c=\frac{100}{0.25}
\]
\[
c=400\,\text{J kg}^{-1}\text{K}^{-1}
\]
The answer is larger than \(C\) numerically because the heat capacity belongs to only \(0.25\,\text{kg}\) of material.
\( \textbf{Final answer:} \) \(c=400\,\text{J kg}^{-1}\text{K}^{-1}\).
220. A coastal region usually has smaller temperature variation than a dry inland region partly because water has:
ⓐ. very small specific heat capacity
ⓑ. zero heat capacity
ⓒ. high specific heat capacity
ⓓ. no ability to absorb heat
Correct Answer: high specific heat capacity
Explanation: Water has a high specific heat capacity compared with many common materials. This means a large amount of heat is needed to produce a small temperature rise in water. During the day, water bodies absorb considerable heat without becoming very hot. At night, they release heat slowly and cool gradually. This moderates the temperature of nearby coastal regions. The effect comes from water’s large heat storage per unit mass per unit temperature change.
