Question

26. (S) Figure shows two spherical containers P and Q
connected by tap T. P contains an ideal gas at
pressure 5 x 105 Nm-2 and temperature 300 K. Q
contains same gas at pressure 2 x 105 Nm-2 and
temperature 400 K. If the tap is opened the final
pressure becomes m * 10Nm? What is the value
of m? The volume of Q is four times the volume
of P:
T
р
Q​

Answer 1

Given that,

Pressure of container P = $5\times10^{5}\ N/m²$

Temperature of container P = 300 K

Pressure of container Q = $2\times10^{5}\ N/m²$

Temperature of container Q = 400 K

The volume of Q is four times the volume  of P.

We need to calculate the value of m

Using formula of number of moles

$initial\ number\ of\ moles = final\ number\ of\ moles$

$\dfrac{P_{P}V_{P}}{RT_{P}}+\dfrac{P_{Q}V_{Q}}{RT_{Q}}=\dfrac{P_{P}V_{P}}{RT_{P}}+\dfrac{P_{Q}V_{Q}}{RT_{Q}}$

Put the value into the formula

$\dfrac{5\times10^{5}\times V_{P}}{300}+\dfrac{2\times10^5\times 4V_{P}}{400}=\dfrac{P\times V}{300}+\dfrac{P\times 4V}{400}$

$\dfrac{5\times10^{5}}{300}+\dfrac{4\times2\times10^{5}}{400}=\dfrac{p}{300}+\dfrac{4p}{400}$

$\dfrac{20\times10^{5}+24\times10^{5}}{1200}=\dfrac{4P+12P}{1200}$

$3666.66\times1200=16P$

$P=\dfrac{3666.66\times1200}{16}$

$P=274999.5\ N/m^2$

$P=2.7\times10^{5}\ N/m^2$

Hence, The value of m is 2.7