A gas is initially at a pressure of 100kPa and its volume is 2.0m… - Vidyadip

Question

A gas is initially at a pressure of $100kPa$ and its volume is $2.0m^3$. Its pressure is kept constant and the volume is changed from $2.0m^3$ to $2.5m^3$. Its volume is now kept constant and the pressure is increased from $100kPa$ to $200kPa$. The gas is brought back to its initial state, the pressure varying linearly with its volume.

Whether the heat is supplied to or extracted from the gas in the complete cycle?
How much heat was supplied or extracted?

✓

Answer

$\text{P}_1 = 100\text{KPa}$

$\text{V}_1=2\text{m}^3$
$\Delta\text{V}_1=0.5\text{m}^3$
$\Delta\text{P}_1 = 100\text{KPa}$
From the graph, We find that area under AC is greater than area under than AB.
So, we see that heat is extracted from the system.

Amount of heat = Area under ABC.

$=\frac{1}{2}\times\frac{5}{10}\times10^5=25000\text{J}$

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