Question

A solid X is in thermal equilibrium with a solid Y, which is at the same temperature as a third solid Z. The three bodies are of different materials and masses. Which one of the following statements is certainly correct? of 164.9J/s, calculate the the thermal conductivity of aluminum
X and Y have the same heat capacity
X and Y have the same internal energy
It is not necessary that Y should be in thermal equilibrium with Z
There is no net transfer of energy if X is placed in thermal contact with Z
14 A hot water tank of heat capacity 5000 JK-1 contains 10 kg of water at 25 °C. What is the time taken to raise the temperature of the water to 45 °C using a heater coil of power of 3.0 kW, given that the specific heat capacity of water is 4200 Jkg-1 K-1?
61 s
280 s
310 s
610 s
15 A solid object M is made of a material with a specific capacity c and a specific latent heat of fusion L.The object is heated up at a constant rate P. Its initial temperature is below its melting point by ΔT. The time for the object to be

Answer 1

Answer on Question #51930-Physics-Field Theory

A solid X is in thermal equilibrium with a solid Y, which is at the same temperature as a third solid Z. The three bodies are of different materials and masses. Which one of the following statements is certainly correct?

X and Y have the same heat capacity

X and Y have the same internal energy

It is not necessary that Y should be in thermal equilibrium with Z

There is no net transfer of energy if X is placed in thermal contact with Z

Solution

X and Z have the same temperature, therefore they would be in thermal equilibrium. If Y is in thermal equilibrium with X, then by the zeroth law of thermodynamics X and Z would also be in thermal equilibrium. Hence there would be no net transfer of heat between X and Z.

Answer: There is no net transfer of energy if X is placed in thermal contact with Z.

14 A hot water tank of heat capacity 5000 JK⁻¹ contains 10 kg of water at 25 °C. What is the time taken to raise the temperature of the water to 45 °C using a heater coil of power of 3.0 kW, given that the specific heat capacity of water is 4200 Jkg⁻¹ K⁻¹?

61 s

280 s

310 s

610 s

Solution

$$Q = P t = m c \Delta T + C \Delta t = (m c + C) \Delta t.$$

So,

$$t = \frac{(m c + C) \Delta T}{P} = \frac{(10 \mathrm{~kg} \cdot 4200 \mathrm{~Jkg}^{-1} \mathrm{K}^{-1} + 5000 \mathrm{~JK}^{-1})(45 - 25) K}{3.0 \cdot 10^{3} \mathrm{W}} = 310 \mathrm{~s}.$$

Answer: 310 s.

15 A solid object M is made of a material with a specific capacity c and a specific latent heat of fusion L. The object is heated up at a constant rate P. Its initial temperature is below its melting point by $\Delta T$. The time for the object to be completely melted is given by

$$\mathrm{M}(\mathrm{c} \Delta \mathrm{T} + \mathrm{L}) / \mathrm{P}$$ $$\mathrm{M}(\mathrm{c} + \mathrm{L}) \Delta \mathrm{T} / \mathrm{P}$$

P/[mΔT(c + L)]

P/[m(cΔT + L)]

Solution

$$Q = P t = M c \Delta T + M L.$$

Thus,

$$t = \frac {M (c \Delta T + L)}{P}.$$

Answer: $\frac{M(c\Delta T + L)}{P}$

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