Question

14 gm of nitrogen gas at constant pressure has temperature of 300 K. How much heat energy would be required to change its temperature to 350 K at same pressure?​

Answer 1

50 k heat energy is required

Answer 2

Given:

Mass of nitrogen gas = 14g

Temperature₁ = 300K

Temperature₂ = 350K

To find:

Amount of heat energy required to rise the temperature.

Solution:

Formula used to calculate the amount of heat energy required to raise the temperature is as follows-

      ΔQ = n$C_p$ΔT

here, ΔQ = amount of heat energy

        n = number of moles

         $C_p$ = Molar specific heat at constant pressure

          ΔT = change in temperature

Firstly, find the number of moles,

       $n = \frac{w}{MM}$

here, n = number of moles

         w = given mass of nitrogen gas = 14 g

         MM = molecular mass of nitrogen gas = 28 gmol⁻¹

by substituting all the values, we get

               $n = \frac{14 g }{28 gmol^-^1}$

              n = 0.5 mol

so, the number of moles of nitrogen is 0.5 mol.

For nitrogen gas, Molar heat capacity at constant pressure is $\frac{7}{2}R$.

Rise in temperature, ΔT = T₂ - T₁

here, T₂ = 350K

        T₁ = 300K

so, ΔT = 350K -300K

     ΔT= 50K

Therefore, total amount of heat will be calculated by substituting all the values as-

      ΔQ = n$C_p$ΔT

      ΔQ = 0.5 × $\frac{7}{2}R$ × 50

      ΔQ = 87.5R

Therefore, the amount of heat supplied to raise the temperature is 87.5R.