Specific heat, calorimetry, change of state and latent heat — practice questions

Question 1 · difficulty L2 · understanding

A water heater of power $2000 \mathrm{~W}$ is used to heat water. The specific heat capacity of water is $4200 \mathrm{~J}$ $\mathrm{kg}^{-1} \mathrm{~K}^{-1}$. The efficiency of heater is $70 \%$. Time required to heat $2 \mathrm{~kg}$ of water from $10^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ is _________ s. (Assume that the specific heat capacity of water remains constant over the temperature range of the water).

Question 2 · difficulty L2 · understanding

A block of ice of mass 120 g at temperature 0$$^\circ$$C is put in 300 g of water at 25$$^\circ$$C. The x g of ice melts as the temperature of the water reaches 0$$^\circ$$C. The value of x is _____________. [Use specific heat capacity of water = 4200 Jkg $$-$$1 K $$-$$1 , Latent heat of ice = 3.5 $$\times$$ 10 5 Jkg $$-$$1 ]

Question 3 · difficulty L2 · understanding

A geyser heats water flowing at a rate of 2.0 kg per minute from 30$$^\circ$$C to 70$$^\circ$$C. If geyser operates on a gas burner, the rate of combustion of fuel will be ___________ g min $$-$$1 . [Heat of combustion = 8 $$\times$$ 10 3 Jg $$-$$1 , Specific heat of water = 4.2 Jg $$-$$1 $$^\circ$$C $$-$$1 ]

Question 4 · difficulty L2 · understanding

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from $27^{\circ} \mathrm{C}$ to $87^{\circ} \mathrm{C}$. The rate of consumption of the gas is $\_\_\_\_$ $\mathrm{g} / \mathrm{s}$. (Take heat of combustion of gas $=5.0 \times 10^4 \mathrm{~J} / \mathrm{g}$ ) specific heat capacity of water $=4200 \mathrm{~J} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$

• A. 4.2
• B. 2.1
• C. 0.21
• D. 0.42

Question 5 · difficulty L2 · understanding

Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. (Take g = 10 m/s 2 , specific heat of water = 4200 J/(kg K))

• A. 0.36 K
• B. 0.23 K
• C. 0.48 K
• D. 0.14 K

Question 6 · difficulty L2 · understanding

$$\text { Match List - I with List - II. }$$ $$\begin{array}{lll} & \text { List - I } & {List - II }\\ \text { } \\ \text { (A) } & \text { Heat capacity of body } & \text { (I) } \mathrm{J} \mathrm{~kg}^{-1} \\ \text { (B) } & \text { Specific heat capacity of body } & \text { (II) } \mathrm{J} \mathrm{~K}^{-1} \\ \text { (C) } & \text { Latent heat } & \text { (III) } \mathrm{J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1} \\ \text { (D) } & \text { Thermal conductivity } & \text { (IV) } \mathrm{J} \mathrm{~m}^{-1} \mathrm{~K}^{-1} \mathrm{~s}^{-1} \end{array}$$ $$\text { Choose the correct answer from the options given below : }$$

• A. (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
• B. (A)-(III), (B)-(I), (C)-(II), (D)-(IV)
• C. (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
• D. (A)-(II), (B)-(III), (C)-(I), (D)-(IV)

Question 7 · difficulty L2 · understanding

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is _______ grams. (Latent heat of fusion of lead $=2.5 \times 10^4 \mathrm{JKg}^{-1}$ and specific heat capacity of lead $=125 \mathrm{JKg}^{-1}$ $\left.\mathrm{K}^{-1}\right)$

• A. 20
• B. 15
• C. 5
• D. 10

Question 8 · difficulty L2 · understanding

Given below are two statements: Statement (I) : Dimensions of specific heat is $$[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}]$$. Statement (II) : Dimensions of gas constant is $$[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}]$$. In the light of the above statements, choose the most appropriate answer from the options given below.

• A. Statement (I) is incorrect but statement (II) is correct
• B. Both statement (I) and statement (II) are incorrect
• C. Both statement (I) and statement (II) are correct
• D. Statement (I) is correct but statement (II) is incorrect

Question 9 · difficulty L2 · understanding

$$0.08 \mathrm{~kg}$$ air is heated at constant volume through $$5^{\circ} \mathrm{C}$$. The specific heat of air at constant volume is $$0.17 \mathrm{~kcal} / \mathrm{kg}^{\circ} \mathrm{C}$$ and $$\mathrm{J}=4.18$$ joule/$$\mathrm{~cal}$$. The change in its internal energy is approximately.

• A. 318 J
• B. 298 J
• C. 284 J
• D. 142 J

Question 10 · difficulty L2 · understanding

A copper block of mass 5.0 kg is heated to a temperature of 500$$^\circ$$C and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper : 0.39 J g $$-$$1 $$^\circ$$C $$-$$1 and latent heat of fusion of water : 335 J g $$-$$1 ]

• A. 1.5 kg
• B. 5.8 kg
• C. 2.9 kg
• D. 3.8 kg