Thermal Properties of Matter Chapter-Wise Test 3

Correct answer Carries: 4.

Wrong Answer Carries: -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?

Given: \( P_1 = 1.9 \, \text{atm} \), \( T_1 = 67^\circ \text{C} = 340 \, \text{K} \), \( V_1 = 6.5 \, \text{L} \), \( P_2 = 2.5 \, \text{atm} \), \( T_2 = 117^\circ \text{C} = 390 \, \text{K} \).

\( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \).

\( V_2 = V_1 \times \frac{P_1}{P_2} \times \frac{T_2}{T_1} = 6.5 \times \frac{1.9}{2.5} \times \frac{390}{340} = 6.5 \times 0.76 \times 1.1471 \approx 5.66 \, \text{L} \).

5.6 L
5.7 L
5.5 L
5.66 L
4

How much heat is required to convert \( 0.2 \, \text{kg} \) of ice at \( -15^\circ \text{C} \) to steam at \( 100^\circ \text{C} \)? (Specific heat of ice = \( 2100 \, \text{J kg}^{-1} \text{K}^{-1} \), latent heat of fusion = \( 3.35 \times 10^5 \, \text{J kg}^{-1} \), specific heat of water = \( 4186 \, \text{J kg}^{-1} \text{K}^{-1} \), latent heat of vaporization = \( 2.256 \times 10^6 \, \text{J kg}^{-1} \))

\( Q_1 = 0.2 \times 2100 \times 15 = 6300 \, \text{J} \) (ice to 0°C).

\( Q_2 = 0.2 \times 3.35 \times 10^5 = 67000 \, \text{J} \) (melting).

\( Q_3 = 0.2 \times 4186 \times 100 = 83720 \, \text{J} \) (water to 100°C).

\( Q_4 = 0.2 \times 2.256 \times 10^6 = 451200 \, \text{J} \) (vaporization).

Total: \( Q = 6300 + 67000 + 83720 + 451200 = 608220 \, \text{J} = 608.22 \, \text{kJ} \).

600 kJ
605 kJ
610 kJ
608.22 kJ
4

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 \( 225 \, \text{cm}^2 \)? (\( \alpha_l = 1.8 \times 10^{-5} \, \text{K}^{-1} \))

Given: \( A_0 = 225 \, \text{cm}^2 \) (one face), total surface area = \( 6 \times 225 = 1350 \, \text{cm}^2 \), \( \Delta T = 135 - 35 = 100^\circ \text{C} \), \( \alpha_l = 1.8 \times 10^{-5} \, \text{K}^{-1} \).

Area expansion: \( \Delta A = A_0 \times 2 \alpha_l \Delta T \).

For total surface area: \( \Delta A = 1350 \times 2 \times 1.8 \times 10^{-5} \times 100 = 1350 \times 3.6 \times 10^{-3} = 4.86 \, \text{cm}^2 \).

4.8 cm²
4.86 cm²
4.9 cm²
5.0 cm²
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? (\( \alpha_l = 1.2 \times 10^{-5} \, \text{K}^{-1} \))

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

\( \Delta A = A_0 \times 2 \alpha_l \Delta T = 625\pi \times 2 \times 1.2 \times 10^{-5} \times 100 \).

\( \Delta A = 625\pi \times 2.4 \times 10^{-3} = 1.5\pi \, \text{cm}^2 \approx 4.71 \, \text{cm}^2 \) (\( \pi \approx 3.14 \)).

4.7 cm²
4.71 cm²
4.8 cm²
4.6 cm²
2

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 = \( 0.25 \times 10^5 \, \text{J kg}^{-1} \))

Given: \( m = 0.4 \, \text{kg} \), \( L_f = 0.25 \times 10^5 = 25000 \, \text{J kg}^{-1} \).

\( Q = m L_f = 0.4 \times 25000 = 10000 \, \text{J} = 10 \, \text{kJ} \).

10 kJ
12 kJ
8 kJ
15 kJ
1

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? (\( \alpha_l = 1.2 \times 10^{-5} \, \text{K}^{-1} \))

Given: \( L_0 = 20 \, \text{cm} \), \( V_0 = 20^3 = 8000 \, \text{cm}^3 \), \( \Delta T = 125 - 25 = 100^\circ \text{C} \), \( \alpha_l = 1.2 \times 10^{-5} \, \text{K}^{-1} \).

\( \alpha_v = 3 \alpha_l = 3 \times 1.2 \times 10^{-5} = 3.6 \times 10^{-5} \, \text{K}^{-1} \).

\( \Delta V = V_0 \alpha_v \Delta T = 8000 \times 3.6 \times 10^{-5} \times 100 = 28.8 \, \text{cm}^3 \).

28 cm³
28.5 cm³
28.8 cm³
29 cm³
3

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?

Given: \( V_1 = 2.5 \, \text{L} \), \( P_1 = 1.2 \, \text{atm} \), \( T_1 = 37^\circ \text{C} = 310 \, \text{K} \), \( P_2 = 2.4 \, \text{atm} \), \( T_2 = 37 + 50 = 87^\circ \text{C} = 360 \, \text{K} \).

\( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \).

\( V_2 = V_1 \times \frac{P_1}{P_2} \times \frac{T_2}{T_1} = 2.5 \times \frac{1.2}{2.4} \times \frac{360}{310} = 2.5 \times 0.5 \times 1.1613 \approx 1.45 \, \text{L} \).

1.4 L
1.5 L
1.45 L
1.6 L
3

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 = \( 4186 \, \text{J kg}^{-1} \text{K}^{-1} \))

Heat lost = Heat gained.

\( 0.25 \times 450 \times (150 - T) = 1.5 \times 4186 \times (T - 30) \).

\( 16875 - 112.5 T = 6279 T - 188370 \).

\( 16875 + 188370 = 6279 T + 112.5 T \).

\( 205245 = 6391.5 T \Rightarrow T \approx 32.11^\circ \text{C} \).

32.11°C
33°C
34°C
31°C
1

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 = \( 386 \, \text{J kg}^{-1} \text{K}^{-1} \))

Given: \( m = 0.5 \, \text{kg} \), \( \Delta T = 80 - 30 = 50^\circ \text{C} \), \( s = 386 \, \text{J kg}^{-1} \text{K}^{-1} \).

\( Q = m s \Delta T = 0.5 \times 386 \times 50 = 9650 \, \text{J} = 9.65 \, \text{kJ} \).

9.5 kJ
9.65 kJ
10 kJ
9 kJ
2

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

At the ice point (freezing of water at standard pressure), Celsius is \( 0^\circ \text{C} \) and Fahrenheit is \( 32^\circ \text{F} \) (Section 10.3).

Both are \( 0^\circ \)
Celsius is \( 32^\circ \), Fahrenheit is \( 0^\circ \)
Celsius is \( -32^\circ \), Fahrenheit is \( 0^\circ \)
Celsius is \( 0^\circ \), Fahrenheit is \( 32^\circ \)
4

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