0 . 056 kg of Nitrogen is enclosed in a vessel at a temperature of 127 ° C . The amount of heat required to double the speed of its molecules is_____ kcal . (Take R = 2 cal mole K - 1 - 1 )

Step-by-step solution

The RMS speed of the molecule is given by v R M S = 3 R T M . Therefore, to double the speed the temperature must become 4 times. Therefore, the change in the temperature is ∆ T = 3 T 0 . Now the process is isochoric (enclosed vessel) therefore, the heat required will be, H = n C v ∆ T ⇒ H = 56 28 × 5 2 R × 3 × 273 + 127 = 12000   cal = 12   kcal