Question

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:

(4) 3000 J​

Explanation:

Given that

Moles =N

At constant volume

We know that heat transfer at constant volume given as

$Q_v=mC_v\Delta T$

m= Mass

Cv = Heat capacity at constant volume

ΔT=Temperature difference

Now by putting the values

$900=mC_v(55-35)$

mCv= 45       ⇒       Cv= 45 /m  

We know that for ideal gas

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

γ = 1.66  for monatomic

So

Cp= 1.66 Cv

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

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

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 correct.

(4) 3000 J​  

Answer 2

Explanation:

Gas. CP. CV. $=CP/CV

Mono. 5/2R 3/2R 5/3

Di. 7/2R 5/2R 7/5

Tri. 4R 3/2R. 4/3