A) \[212\,kPa\]
B) \[209\,kPa\]
C) \[206\,kPa\]
D) \[200\,kPa\]
Correct Answer: B
Solution :
The ideal gas law is the equation of state of an ideal gas. The state of an amount of gas is determined by its pressure, volume and temperature . The equation has the form \[pV=nRT\] where, p is pressure, V the volume, \[n\]the number of moles, R the gas constant and T the temperature. \[\therefore \] \[\frac{{{p}_{1}}{{V}_{1}}}{{{T}_{1}}}=\frac{{{p}_{2}}{{V}_{2}}}{{{T}_{2}}}\] Given, \[{{p}_{1}}=200\,kPa,{{V}_{1}}=V,\] Given, \[{{p}_{1}}=200\,kPa,\,{{V}_{1}}=V,\] \[{{T}_{1}}=273+22=295\,K,\] \[{{V}_{2}}=V+0.02V,{{T}_{2}}=273+42=315\,K\] \[\frac{220\times V}{295}=\frac{{{p}_{2}}\times 1.02V}{315}\] \[\Rightarrow \] \[{{p}_{2}}=\frac{200\times 315}{295\times 1.02}\] \[{{p}_{2}}\approx 209\,kPa\]
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