Concepts Of Physics MCQ Edition [Volume 1]PhysicsIntroduction to Physics
Find the dimensions of the gas constant R . An equation involving this quantity is PV = nRT .
Options
- AM L T⁻² K⁻¹ ( mol )⁻¹
- BML^2 T⁻² K⁻¹ ( mol )⁻¹
- CML^2 T⁻¹ K⁻¹ ( mol )⁻¹
- DML^2 T⁻² K⁻¹
Correct answer
B. ML^2 T⁻² K⁻¹ ( mol )⁻¹
Step-by-step solution
The ideal gas equation is given by PV = nRT . Rearranging for the gas constant R , we get: R = PV nT The dimensions of pressure P (Force/Area) are [M L⁻¹ T⁻²] . The dimensions of volume V are [L^3] . The dimensions of number of moles n are [ mol ] and temperature T are [K] . Substituting these dimensions into the equation for R , we get: [R] = [M L⁻¹ T⁻²][L^3] [ mol ][K] [R] = [M L^2 T⁻² K⁻¹ ( mol )⁻¹]