Question

14. N moles of an ideal monatomic gas is heated from
35°C to 55°C at constant volume and 900 J of heat
is absorbed. If same gas is heated at constant
pressure from 55°C to 95°C, then the heat required
will be
(1) 1000 J
(2) 1500 J
(3) 2000 J
(4) 3000 J​

Answer 1

Answer:

3000 is the right answer

Answer 2

(4) 3000 J​

Explanation:

Given that

Moles =N

Lets M= molecular weight

So mass ,m = N .M

As we know that heat transfer at constant volume given as

$Q_v=mC_v\Delta T$

Qv= Heat transfer at constant volume

m= Mass

Cv = Heat capacity at constant volume

ΔT=Temperature difference

Here ΔT= 55 - 35 = 20°C

Q= 900 J

By putting the values in the above equation

$900=mC_v(55-35)$

mCv= 45       ⇒       Cv= 45 /m  

As we know that for ideal gas

$\dfrac{C_p}{C_v}=\gamma$

γ = 1.66  for monatomic

So

Cp= 1.66 Cv

$C_p=\dfrac{1.66\times 45}{m}$

$C_p=\dfrac{74.7}{m}$

We know that at constant pressure heat transfer given as

$Q_p=mC_p\Delta T$

Here ΔT = 95-55 = 40°C

$Q_p=m\times \dfrac{74.7}{m}\times 40$

Qp= 2988 J ≅3000 J

So the option (4) is right.

(4) 3000 J​