First slide

Heat ;work and internal energy

Question

One mole of an ideal gas at temperature T₁ expand according to the $l a w (p / v) = c o n s \tan t .$ Find the work done when the final temperature become T₂:

Moderate

A

$R (T_{2} - T_{1})$
B

$\frac{R}{2} (T_{2} - T_{1})$
C

$\frac{R}{4} (T_{2} - T_{1})$
D

$P V (T_{2} - T_{1})$

Solution

$\begin{array}{l} W = \int_{v_{1}}^{v_{2}} P d V = \int_{v_{1}}^{v_{2}} V d V \\ ∴ W = \frac{1}{2} k [v_{2}^{2} - v_{1}^{2}] \\ P V = R T But P = kv \\ ∴ {kv}^{2} = R T \\ Or k (v_{2}^{2} - v_{1}^{2}) = R (T_{2} - T_{1}) \\ W = \frac{R}{2} (T_{2} - T_{1}) \end{array}$

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