NEET Thermal Properties of Matter — Set 5

Question 1

A $ 0.2 \, \text{kg} $ aluminium block at $ 120^\circ \text{C} $ is placed in $ 0.8 \, \text{kg} $ of water at $ 20^\circ \text{C} $ in a $ 0.1 \, \text{kg} $ copper calorimeter at $ 20^\circ \text{C} $. What is the final temperature? (Specific heat of aluminium = $ 900 \, \text{J kg}^{-1} \text{K}^{-1} $, water = $ 4186 \, \text{J kg}^{-1} \text{K}^{-1} $, copper = $ 386 \, \text{J kg}^{-1} \text{K}^{-1} $)

Accepted Answer

Heat lost = Heat gained. $ 0.2 \times 900 \times (120 - T) = (0.8 \times 4186 + 0.1 \times 386) \times (T - 20) $. $ 21600 - 180 T = (3348.8 + 38.6) \times (T - 20) = 3387.4 T - 67748 $. $ 21600 + 67748 = 3387.4 T + 180 T $. $ 89348 = 3567.4 T \Rightarrow T \approx 25.04^\circ \text{C} \approx 25^\circ \text{C} $.

Question 2

A silver sphere of radius $ 8 \, \text{cm} $ at $ 70^\circ \text{C} $ is cooled to $ 20^\circ \text{C} $. What is the decrease in its volume? ($ \alpha_l = 1.9 \times 10^{-5} \, \text{K}^{-1} $)

Accepted Answer

Given: $ r = 8 \, \text{cm} $, $ V_0 = \frac{4}{3} \pi \times 8^3 = \frac{2048}{3} \pi \, \text{cm}^3 $, $ \Delta T = 20 - 70 = -50^\circ \text{C} $, $ \alpha_l = 1.9 \times 10^{-5} \, \text{K}^{-1} $. $ \alpha_v = 3 \alpha_l = 3 \times 1.9 \times 10^{-5} = 5.7 \times 10^{-5} \, \text{K}^{-1} $. $ \Delta V = V_0 \alpha_v \Delta T = \frac{2048}{3} \pi \times 5.7 \times 10^{-5} \times (-50) $. $ \Delta V = \frac{2048}{3} \pi \times (-2.85 \times 10^{-3}) \approx -6.12 \pi \approx -19.22 \, \text{cm}^3 $ (decrease of $ 19.22 \, \text{cm}^3 $).

Question 3

What is the key difference between Celsius and Fahrenheit scales at the boiling point of water?

Accepted Answer

At the boiling point of water under standard pressure, the Celsius scale reads $ 100^\circ \text{C} $, while the Fahrenheit scale reads $ 212^\circ \text{F} $, reflecting different interval sizes and zero points.

NEET Physics: Thermal Properties of Matter — Practice Set 5

Q2. A silver sphere of radius \( 8 \, \text{cm} \) at \( 70^\circ \text{C} \) is cooled to \( 20^\circ \text{C} \). What is the decrease in its volume? (\( \alpha_l = 1.9 \times 10^{-5} \, \text{K}^{-1} \))

Q3. What is the key difference between Celsius and Fahrenheit scales at the boiling point of water?

Q5. A steel rod has a length of \( 1 \, \text{m} \) at \( 20^\circ \text{C} \). What will be its length at \( 120^\circ \text{C} \) if the coefficient of linear expansion of steel is \( 1.2 \times 10^{-5} \, \text{K}^{-1} \)?

Q6. How much heat is needed to convert \( 0.2 \, \text{kg} \) of water at \( 100^\circ \text{C} \) to steam at \( 100^\circ \text{C} \)? (Latent heat of vaporization = \( 2.256 \times 10^6 \, \text{J kg}^{-1} \))

Q7. What is the Kelvin temperature equivalent to \( -23^\circ \text{C} \)?

Q8. Which of the following is true about latent heat during a phase change?

Q9. What is the relationship between the Celsius and Kelvin scales?

Q10. How much heat is required to melt \( 0.3 \, \text{kg} \) of ice at \( 0^\circ \text{C} \) to water at \( 0^\circ \text{C} \)? (Latent heat of fusion = \( 3.33 \times 10^5 \, \text{J kg}^{-1} \))