An inflated rubber balloon contains one mole of an ideal gas, has a pressure P, volume V and temperature T. If the temperature rises to 1.1 T, and the volume is increased to 1.05 V, the final pressure will be

Question

An inflated rubber balloon contains one mole of an ideal gas, has a pressure P, volume V and temperature T. If the temperature rises to 1.1 T, and the volume is increased to 1.05 V, the final pressure will be (A) 1.1 P (B) P (C) less than P (D) between P and 1.1 P

Tardigrade Admin · Accepted Answer

Using PV = nRT or (P1 V1/T1 ) = (P2 V2/T2 ) Here, P1 = P, V1 = V, T1 = T, T2 = 1.1 T and V2 = 1.05 V ∴ P2 = (P1 V1 T2/V2T1) = (P× V × 1.1 T/1.05 V × T) = 1.05 P

Q. An inflated rubber balloon contains one mole of an ideal gas, has a pressure $P$ , volume $V$ and temperature $T$ . If the temperature rises to $1.1 T$ , and the volume is increased to $1.05 V$ , the final pressure will be

$1.1 P$

$P$

less than $P$

between $P$ and $1.1 P$

Using $P V = n RT$ or $\frac{P _{1} V _{1}}{T _{1}} = \frac{P _{2} V _{2}}{T _{2}}$
Here, $P_{1} = P$ , $V_{1} = V$ , $T_{1} = T$ , $T_{2} = 1.1 T$ and $V_{2} = 1.05 V$
$∴ P_{2} = \frac{P _{1} V _{1} T _{2}}{V _{2} T _{1}} = \frac{P \times V \times 1.1 T}{1.05 V \times T} = 1.05 P$

Q. An inflated rubber balloon contains one mole of an ideal gas, has a pressure P, volume V and temperature T. If the temperature rises to 1.1T, and the volume is increased to 1.05V, the final pressure will be

1.1P

P

less than P

between P and 1.1P

Using PV=nRT or T1​P1​V1​​=T2​P2​V2​​ Here, P1​=P, V1​=V, T1​=T, T2​=1.1T and V2​=1.05V ∴P2​=V2​T1​P1​V1​T2​​=1.05V×TP×V×1.1T​=1.05P

Q. An inflated rubber balloon contains one mole of an ideal gas, has a pressure $P$ , volume $V$ and temperature $T$ . If the temperature rises to $1.1 T$ , and the volume is increased to $1.05 V$ , the final pressure will be

$1.1 P$

$P$

less than $P$

between $P$ and $1.1 P$

Using $P V = n RT$ or $\frac{P _{1} V _{1}}{T _{1}} = \frac{P _{2} V _{2}}{T _{2}}$
Here, $P_{1} = P$ , $V_{1} = V$ , $T_{1} = T$ , $T_{2} = 1.1 T$ and $V_{2} = 1.05 V$
$∴ P_{2} = \frac{P _{1} V _{1} T _{2}}{V _{2} T _{1}} = \frac{P \times V \times 1.1 T}{1.05 V \times T} = 1.05 P$