# when an ideal diatomic gas is heated at constant pressure. the fraction of heat energy supplied which increases the internal energy of the gas is

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## When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is

Byju's Answer Standard XII Physics

Equipartition Theorem

When an ideal... Question

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is

A B C D Open in App Solution

The correct option is **D**

Fraction of supplied energy which in creases the internal energy is given by

f = △ U ( △ Q ) F = ( △ Q ) V ( △ Q ) F = μ C V △ T μ C F △ T = 1 γ For diatomic gas γ = 7 5 ⇒ f = 5 7 Suggest Corrections 6

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## When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increased the internal energy of the gas is:(A). $\\dfrac{2}{5}$(B). $\\dfrac{3}{5}$(C). $\\dfrac{3}{7}$(D). $\\dfrac{5}{7}$

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increased the internal energy of the gas is:(A). $\\dfrac{2}{5}$(B). $\\dfrac{3}{5}$(C). $\\dfrac{3}{7}$(D). $\\dfrac{5}{7}$ . Ans: Hint: These ...

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increased the internal energy of the gas is:(A). 2 5 25 (B). 3 5 35 (C). 3 7 37 (D). 5 7 57

Last updated date: 12th Mar 2023

• Total views: 291.6k • Views today: 4.71k Answer Verified 291.6k+ views

Hint: These types of question follows the basic patterns; you just have to remind some basic formulas for example

C v = f 2 Cv=f2 and C p = f 2 +1 Cp=f2+1 also the formula C v C p = 1 γ CvCp=1γ

to find the correct option.

Complete step-by-step solution -

Total heat energy supplied to raise a diatomic gas's temperature at constant pressure =

n C p △T nCp△T

And the total rise in internal energy =

n C v △T nCv△T

Thus, fraction of heat energy utilized in increasing internal energy =

n C v △T n C p △T nCv△TnCp△T (equation 1)

Simplifying equation 1

⇒ ⇒ C v C p = f 2 f 2 +1 CvCp=f2f2+1 Since we know that C v = f 2 Cv=f2 and C p = f 2 +1 Cp=f2+1 ⇒ ⇒ C v C p = f f+2 CvCp=ff+2 (Equation 2)

Here f is the number of degrees of freedom of the gas and here for diatomic gas f = 5.

Substituting the value of f in the equation 2

⇒ ⇒ C v C p = 5 5+2 CvCp=55+2 Since C v C p = 1 γ CvCp=1γ Therefore 1 γ = 5 7 1γ=57

is a fraction of the heat energy supplied which increases the internal energy of the gas.

Hence, D is the correct option.

Note: We have noticed that the term internal energy of an ideal gas is the main concept in this question and it can be explained as the internal changes in energy in an ideal gas can be represented only by changes in its kinetic energy. Kinetic energy is simply the perfect gas’s internal energy and depends entirely on its pressure, volume, and thermodynamic temperature. An ideal gas's intrinsic energy is proportional to its mass (number of moles) n and its temperature T.i.e.

U=cnT U=cnT

## When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied, which increases the internal energy of the gas, is

The desired fraction is f=(DeltaU)/(DeltaQ)=(nCVDeltaT)/(nCpDeltaT)=(CV)/(Cp)=1/gamma or f=5/7 (as gamma=7/5) Therefore, the correct option is (d).

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied, which increases the internal energy of the gas, is

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Transcript

hello sir question is when ideal diatomic gas is heated at constant pressure the fraction of heat energy supplied with increases the internal energy of the ok so we have been given the question that men are diatomic ideal gas is heated at constant pressure then what will be the fraction of heat energy supplied which increases the internal energy ok Shruti fraction f will be Delta UEFA Delta q and a l u is nothing but ncv X Delta T / will take us NCP Delta T from here and got cancelled out and Delta ticket cancelled out so what we get is CV upon CP and CV for SIP is nothing but one upon the ideal gas is a diatomic gas and as we know that Gamma for diatomic gas is 7 upon 5

diatomic gas putting the value what we get is this fraction of the increase in the internal energy to heat supplied and it will come out 5 by 7 from the options but we says I oughta know before is the correct option for thank you

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