Question 506: Thermodynamics & KTG

Question

5 moles of unknown gas is heated at constant volume from 10°C to 20°C. The molar specific heat of this gas at constant pressure $c_p = 8$ cal/mol.°C and $R = 8.36$ J/mol.°C. The change in the internal energy of the gas is __________ calorie.

Accepted Answer

In a P-V diagram (Pressure vs. Volume), the total work done during a cyclic process is equivalent to the area enclosed by the cycle.
The cycle $\mathrm{A} ightarrow \mathrm{B} ightarrow \mathrm{C} ightarrow \mathrm{A}$ is moving in a clockwise direction.
In a clockwise cycle on a P-V diagram, the work done by the system is positive.
The area enclosed by the triangle ABC is calculated using the formula for the area of a right-angled triangle:
$$ \begin{aligned} & 	ext { Work Done }=	ext { Area }=\frac{1}{2} 	imes 	ext { Base ÃÂ Height } \ & 	ext { Base }=V_C-V_A=5 \mathrm{~m}^3-2 \mathrm{~m}^3=3 \mathrm{~m}^3 \ & 	ext { Height }=P_B-P_C=300 \mathrm{~Pa}-100 \mathrm{~Pa}=200 \mathrm{~Pa} \end{aligned} $$
Substituting the values into the area formula:
$$ 	ext { Work Done }=\frac{1}{2} 	imes 3 \mathrm{~m}^3 	imes 200 \mathrm{~Pa}=300 \mathrm{~J} $$
Therefore, the total work done by the system during the cycle ABC is 300 J . Hence, the correct answer is $\mathbf{3 0 0}$.

Thermodynamics & KTG

5 moles of unknown gas is heated at constant volume from 10°C to 20°C. The molar specific heat of this gas at constant pressure c_p = 8 cal/mol.°C and R = 8.36 J/mol.°C. The change in the internal energy of the gas is __________ calorie.

Integer / Numeric Answer Type