Thermodynamics!

Here is a question,

When an ideal gas undergoes an adiabatic change causing a temperature change $\Delta T$

(A)there is no heat gained or lost by the gas

(B)the work done by the gas is equal to change in internal energy

(C)the change in internal energy per mole of the gas is ${ C }_{ v }\Delta T$ , where ${ C }_{ v }$ is the molar heat capacity at constant volume.

The given answer is A and C.

Why is B not correct?

Here is why I think so,

Since $\Delta Q=0$ for adiabatic process, $0=\Delta U+\Delta W$ $\Longrightarrow -\Delta U=\Delta W$ $\therefore$ Work done by the gas is equal to change in internal energy.

#Mechanics

Easy Math Editor

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Comments

Work done is not equal to change in internal energy, you have to consider the signs as well. If internal energy change is positive,work done is negative and vice versa.

A Former Brilliant Member - 5 years, 2 months ago

Thanks!

Anandhu Raj - 5 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$