# Question #c03d7

Mar 16, 2016

3.

#### Explanation:

From State 1 to State 2 it is given that the $P V$ graph has been obtained while given mass of gas was subjected to temperature changes. We see that from state 1 to 2 both Pressure and Volume are changing.

We need to consider case under Ideal gas equation
$P V = n R T$
where $P$, is the pressure, $V$ is the volume, $n$ is the number of moles, $T$ is the temperature of the gas in Kelvin and $R$ is the gas constant.

From the gas equation we obtain

$\frac{P V}{T} = n R$
is a Constant for a sample of gas.

It is given that the sample is being subjected to temperature changes and no effort is made to control either pressure or the volume of the sample.

Let us concentrate in the immediate vicinity of the point 1 in the graph. Here $P$ is decreasing and $V$ is increasing. It is safe to assume that near this point gas sample is expanding and not being compressed. We know that for adiabatic expansion the temperature of the sample decreases. This in turn would result in steeper fall in pressure. As such a drop is not seen we can infer that the sample is being heated at the point of interest.

This inference excludes options 2 and 4 as being not correct.
For considering options 1 and 3 beyond point 1, recall the Gas equation above.

For option 1: Heated continuously.

At some point while going from state 1 to state 2 we could observe both pressure and volume increasing to offset the changes in the temperature due to heating of the sample. As such a point is not there in the graph, therefore this option is not correct option.

For option 3: Heated in the beginning and cooled towards the end.

Either both pressure and volume could decrease or either of the two increase while other decreased to offset the changes in the temperature due to cooling of the sample. This option appears the only option consistent with the graph.