Two vessels with adiabatic walls are shown in the figure. One vessel holds 0.1 g of helium ( = 1.67 , M = 4 g mol ⁻¹ ) while the other holds an unknown amount of hydrogen ( = 1.4 , M = 2 g mol ⁻¹ ). The initial temperatures of both gases are identical. They are electrically heated for a certain duration, supplying equal amounts of heat to each gas. If the temperature of both gases increases by the exact same amount,

Step-by-step solution

Since the gases are heated in closed vessels, the process is isochoric (constant volume). The heat supplied at constant volume is given by: Q = n C_v T Given that equal amounts of heat are supplied ( Q_ He = Q_ H₂ ) and the temperature increase is the same ( T_ He = T_ H₂ ), we have: n_ He C_ v,He = n_ H₂ C_ v,H₂ We know that C_v = R - 1 and n = m M . For Helium (monoatomic): m_ He = 0.1 g , M_ He = 4 g mol ⁻¹ , _ He = 1.67 5 3 C_ v,He = R 5 3 - 1 = 3 2 R For Hydrogen (diatomic): M_ H₂ = 2 g mol ⁻¹ , _ H₂ = 1.4 = 7