First slide

Heat ;work and internal energy

Question

What amount of heat is needed to raise the temperature of $2 \times 10^{- 2} k g$ of nitrogen at room temperature to raise it’s temperature by 45° C at constant pressure?(given molecular mass=28 and R=8.3 J $m o l^{- 1} K^{- 1}$ ; $C_{p} =7R/2$ )

Moderate

A

9.33 cal
B

93.3 J
C

933.7 J
D

933.3 cal

Solution

number of moles $n= \frac{m}{M} = \frac{20}{28} = 0.174$
where m is mass of gas in gram=0.02kg=0.02x1000g=20g
M is molecular weight of gas
$\begin{array}{rcl} m o l a r s p e c i f i c h e a t o f g a s a t c o n s \tan t p r e s s u r e i s C_{p} \\ C_{p} =7R/2= \frac{7}{2} \times 8.3 {J mole}^{-1} K^{- 1} \\ a m o u n t o f h e a t r e q u i r e d t o r a i s e t e m p e r a t u r e o f g a s a t c o n s \tan t p r e s s u r e i s Q \\ {Q=nC}_{p} \times ΔT \\ h e r e ΔT is raise in temperature \\ s u b s t i t u t e t h e v a l u e s o f n, C_{p}, ΔT \\ Q =0.714 \times \frac{7}{2} \times 8.3 \times 45 J \\ \Rightarrow & Q = 933.75 J \end{array}$

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