We know that, Q = nC_pdT… (i),

Where

Q = heat required to raise the temperature

n = number of moles

C_p = specific heat capacity at constant pressure

dT = rise in temperature.

In this first case,

Amount of heat required(Q) = 70 cal

Number of moles(n) = 2 mol

Rise in temperature(dT) = (35-30)⁰C = 5⁰C

Hence, from (i), we get C_p = 7 calmol^{-1 0}C^-1

Now, we know, C_p - C_v = R,

Where

C_p = specific heat capacity at constant pressure

C_v = specific heat capacity at constant volume

R = universal gas constant = 1.98 calmol^{-1 0}C^-1

Therefore, we get C_v = C_p - R = (7-1.98) cal mol^{-1 0}C^-1

= 5.02 cal mol^{-1 0}C^-1

Now, in the new case, change in temperature dT = 5⁰C as before. Number of moles(n) = 2, and C_v = 5.02 calmol^{-1 0}C^-1

Hence, amount of heat required to raise the temperature of the same gas through the same range

dQ = nCvdT = (2 x 5.02 x 5) cal = 50.2 cal which is approximately equal to 50 cal.

Hence, the correct option is (b).