Question

Heat is supplied to a sample of a monatomic ideal gas at 40 °C. It is observed that the gas expands until its volume is doubled and the pressure drops to half of its original value. What is the final temperature of the gas?

Answer 1

Answer:

 40 °C.        

Explanation:

Given that

Initial temperature ,T=40 + 273 = 313 K

Initial pressure = P₁

Initial volume = V₁

Final volume = V₂ = 2 V₁

Final pressure =P₂

$P_2=\dfrac{P_1}{2}$

Lets take final temperature = T₂

We know that ideal gas equation

P V= m RT

Where ,P=Pressure ,V=Volume ,m=mass ,R=Gas constant , = Temperature

By using mass conservation

$\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}$

$T_2=\dfrac{P_2V_2}{P_1V_1}\times T_1$

Now by putting the values in the above equation we get

$T_2=\dfrac{0.5\times P_1\times 2\times V_1}{P_1V_1}\times 313$

$T_2 = 1\times 313\ K$

$T_2=313 K$

Therefore the final temperature will be 313 K or 40 °C.