NEET Thermal Properties of Matter — Set 3

Question 1

A gas at $ 1.9 \, \text{atm} $ and $ 67^\circ \text{C} $ occupies $ 6.5 \, \text{L} $. If the pressure is increased to $ 2.5 \, \text{atm} $ and temperature raised to $ 117^\circ \text{C} $, what is the new volume?

Accepted Answer

Given: $ P_1 = 1.9 \, \text{atm} $, $ T_1 = 67^\circ \text{C} = 340 \, \text{K} $, $ V_1 = 6.5 \, \text{L} $, $ P_2 = 2.5 \, \text{atm} $, $ T_2 = 117^\circ \text{C} = 390 \, \text{K} $. $ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} $. $ V_2 = V_1 \times \frac{P_1}{P_2} \times \frac{T_2}{T_1} = 6.5 \times \frac{1.9}{2.5} \times \frac{390}{340} = 6.5 \times 0.76 \times 1.1471 \approx 5.66 \, \text{L} $.

Question 2

A steel disc of radius $ 25 \, \text{cm} $ at $ 30^\circ \text{C} $ is heated to $ 130^\circ \text{C} $. What is the increase in its area? ($ \alpha_l = 1.2 \times 10^{-5} \, \text{K}^{-1} $)

Accepted Answer

Given: $ r = 25 \, \text{cm} $, $ A_0 = \pi r^2 = \pi \times 25^2 = 625\pi \, \text{cm}^2 $, $ \Delta T = 130 - 30 = 100^\circ \text{C} $, $ \alpha_l = 1.2 \times 10^{-5} \, \text{K}^{-1} $. $ \Delta A = A_0 \times 2 \alpha_l \Delta T = 625\pi \times 2 \times 1.2 \times 10^{-5} \times 100 $. $ \Delta A = 625\pi \times 2.4 \times 10^{-3} = 1.5\pi \, \text{cm}^2 \approx 4.71 \, \text{cm}^2 $ ($ \pi \approx 3.14 $).

Question 3

What is the heat required to raise the temperature of $ 0.5 \, \text{kg} $ of copper from $ 30^\circ \text{C} $ to $ 80^\circ \text{C} $? (Specific heat of copper = $ 386 \, \text{J kg}^{-1} \text{K}^{-1} $)

Accepted Answer

Given: $ m = 0.5 \, \text{kg} $, $ \Delta T = 80 - 30 = 50^\circ \text{C} $, $ s = 386 \, \text{J kg}^{-1} \text{K}^{-1} $. $ Q = m s \Delta T = 0.5 \times 386 \times 50 = 9650 \, \text{J} = 9.65 \, \text{kJ} $.

NEET Physics: Thermal Properties of Matter — Practice Set 3

Q1. A gas at \( 1.9 \, \text{atm} \) and \( 67^\circ \text{C} \) occupies \( 6.5 \, \text{L} \). If the pressure is increased to \( 2.5 \, \text{atm} \) and temperature raised to \( 117^\circ \text{C} \), what is the new volume?

Q2. A steel disc of radius \( 25 \, \text{cm} \) at \( 30^\circ \text{C} \) is heated to \( 130^\circ \text{C} \). What is the increase in its area? (\( \alpha_l = 1.2 \times 10^{-5} \, \text{K}^{-1} \))

Q3. What is the heat required to raise the temperature of \( 0.5 \, \text{kg} \) of copper from \( 30^\circ \text{C} \) to \( 80^\circ \text{C} \)? (Specific heat of copper = \( 386 \, \text{J kg}^{-1} \text{K}^{-1} \))

Q4. A \( 0.25 \, \text{kg} \) iron block at \( 150^\circ \text{C} \) is dropped into \( 1.5 \, \text{kg} \) of water at \( 30^\circ \text{C} \). What is the final temperature? (Specific heat of iron = \( 450 \, \text{J kg}^{-1} \text{K}^{-1} \), water = \( 4186 \, \text{J kg}^{-1} \text{K}^{-1} \))

Q5. How much heat is needed to melt \( 0.4 \, \text{kg} \) of lead at its melting point of \( 328^\circ \text{C} \)? (Latent heat of fusion of lead = \( 0.25 \times 10^5 \, \text{J kg}^{-1} \))

Q6. A brass cube of side \( 15 \, \text{cm} \) at \( 35^\circ \text{C} \) is heated to \( 135^\circ \text{C} \). What is the increase in its surface area if one face is \( 225 \, \text{cm}^2 \)? (\( \alpha_l = 1.8 \times 10^{-5} \, \text{K}^{-1} \))

Q8. A steel cube of side \( 20 \, \text{cm} \) at \( 25^\circ \text{C} \) is heated to \( 125^\circ \text{C} \). What is the increase in volume? (\( \alpha_l = 1.2 \times 10^{-5} \, \text{K}^{-1} \))

Q9. A gas occupies \( 2.5 \, \text{L} \) at \( 1.2 \, \text{atm} \) and \( 37^\circ \text{C} \). If the pressure is doubled and temperature increased by \( 50^\circ \text{C} \), what is the new volume?

Q10. Which of the following is true about the Celsius and Fahrenheit scales at the ice point?