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Heat Transfer

In the given ...

Question

In the given graph an ideal gas change its state from A to state C by two paths ABC and AC.

The internal energy of gas at state B is 20 J. The amount of heat (in J) supplied to the gas to go from A to B is $2 \times X$ .Then value of x is;

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Solution

$Q_{B A} = U_{B A} + W_{B A}$
It is an isochoric process so work done will be zero.
Now,
$Q_{B A} = U_{A} - U_{B}$
$T_{A} = \frac{20}{n R}$ ------ $(P V = n R T)$
$U_{A} = 1.5 n R T_{A} = 30 J o u l e$
SO $Q_{B A} = 30 - 20 = 10 J o u l e$

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