Volume versus temperature graphs for a given mass of an ideal gas are shown in figure. At two different values of constant pressure. What can be inferred about relation between `P_(1)` and `P_(2)` ?

Options

A. `p_1gtp_2`
B. `p_1=p_2`
C. `p_1ltp_2`
D. Data is insufficient

Answer

A

Explanation

We know for an ideal gas,
`pV=nRTrArrV=((nR)/p)T`
Slope of the V - T graph, `m=(dV)/(dT)=(nR)/p`
[m = slope of V - t graph]
`rArrm prop 1/p" "[thereforenR= "constant"]`
`rArrp prop 1/m`
hence `p_1/p_2=m_2/m_1 [{:("p=pressure"),("V=volume"),("n=number of moles of gases"),("R=gas constant"),("T=temperature"):}]`
Where `m_1` is slope of the graph corresponding to `p_1` and similarly `m_2` is slope corresponding to `p_2`
`rArrp_2ltp_1 or p_1gtp_2`