MHT CET · Physics · Thermodynamics
A container A contains an ideal gas at pressure P' volume ' \(\mathrm{V}\) ' and temperature ' \(\mathrm{T}\) '. A second container B contains the same gas at pressure ' \(2 \mathrm{P}\) ', volume ' \(2 \mathrm{~V}\) ' and temperature \(\frac{\mathrm{T}}{2}\). The ratio of mass of gas in \(\mathrm{A}\) to that in \(\mathrm{B}\) is
- A \(1: 4\)
- B \(1: 8\)
- C \(1: 1\)
- D \(1: 2\)
Answer & Solution
Correct Answer
(B) \(1: 8\)
Step-by-step Solution
Detailed explanation
Ideal gas equation is:
\(\mathrm{PM}=\rho \mathrm{RT}\)
\(\rho=\left(\frac{\mathrm{m}}{\mathrm{v}}\right)=\left(\frac{\text { mass }}{\text { volume }}\right), \mathrm{M}\) is molecular weight.
Taking ratio of \(\mathrm{eq}^{\mathrm{n}}(1) \&(2)\)
\(\frac{\mathrm{m}_{\mathrm{A}}}{\mathrm{m}_{\mathrm{B}}}=\frac{1}{8}\)
\(\mathrm{PM}=\rho \mathrm{RT}\)
\(\rho=\left(\frac{\mathrm{m}}{\mathrm{v}}\right)=\left(\frac{\text { mass }}{\text { volume }}\right), \mathrm{M}\) is molecular weight.
Taking ratio of \(\mathrm{eq}^{\mathrm{n}}(1) \&(2)\)
\(\frac{\mathrm{m}_{\mathrm{A}}}{\mathrm{m}_{\mathrm{B}}}=\frac{1}{8}\)
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