Question 49: Thermodynamics & KTG

Question

A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure below. It absorbs 60 J of heat during the part AB and rejects 80 J of heat during CA . There is no heat exchanged during the process $\mathrm{BC} . \mathrm{A}$ work of 40 J is done on the gas during the part BC . If the internal energy of the gas at A is 1450 J , then the work done by the gas during the part CA is:

Accepted Answer

The coefficient of volume expansion ($$\beta$$) is given as $$49 	imes 10^{-5} \mathrm{~K}^{-1}$$. The formula to determine the change in volume due to thermal expansion is:
$$ \Delta V = V \beta \Delta T $$
Here:
$$\Delta V$$ is the change in volume.
$$V$$ is the original volume.
$$\beta$$ is the coefficient of volume expansion.
$$\Delta T$$ is the change in temperature.
Given that the temperature change ($$\Delta T$$) is $$50^{\circ} \mathrm{C}$$, we have:
$$ \Delta V = V \cdot (49 	imes 10^{-5} \mathrm{~K}^{-1}) \cdot 50 $$
$$ \Delta V = V \cdot (49 	imes 10^{-5} 	imes 50) $$
$$ \Delta V = V \cdot (2450 	imes 10^{-5}) $$
$$ \Delta V = V \cdot 0.0245 $$
This indicates that the volume increases by 2.45%. Since density ($$ho$$) is inversely proportional to volume ($$V$$), a 2.45% increase in volume will result in a 2.45% decrease in density.
Thus, the percentage change in density is 2.45%. Hence, the correct option is:
Option D: 2.45

Answer

10J

Answer

20J

Answer

40J

Answer

30J

Thermodynamics & KTG

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