Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Heat and Thermodynamics question

2017 · 8 Apr · Shift 1 · Q62
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Heat and Thermodynamics
  5. /2017 · 8 Apr · Shift 1 · Q62

Heat and Thermodynamics question

2017 · 8 Apr · Shift 1 · Q62

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (Cp ) and at constant volume (Cv) is :
  1. A
    6
  2. B
    72{7 \over 2}27​
  3. C
    52{5 \over 2}25​
  4. D
    75{7 \over 5}57​
View written solutionFree

Correct answer: D

  1. Use degrees of freedom to find CvC_vCv​

For an ideal gas with fff degrees of freedom, Cv=f2RC_v = \frac{f}{2}RCv​=2f​R

Given f=5f=5f=5, Cv=52RC_v = \frac{5}{2}RCv​=25​R

  1. Find CpC_pCp​

For an ideal gas, Cp=Cv+RC_p = C_v + RCp​=Cv​+R

So, Cp=52R+R=72RC_p = \frac{5}{2}R + R = \frac{7}{2}RCp​=25​R+R=27​R

  1. Compute the ratio

The ratio of specific heats is γ=CpCv\gamma = \frac{C_p}{C_v}γ=Cv​Cp​​

Thus, γ=72R52R=75\gamma = \frac{\frac{7}{2}R}{\frac{5}{2}R} = \frac{7}{5}γ=25​R27​R​=57​

  1. Check options
  • A: 666 ❌
  • B: 72\frac{7}{2}27​ ❌
  • C: 52\frac{5}{2}25​ ❌
  • D: 75\frac{7}{5}57​ ✅

Hence, the correct answer is D.

PreviousNext

More from Heat and Thermodynamics

  • A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by Δ T. The net change in its length is zero. Let ℓ be the length of the rod, A its…2017 · MCQ
  • In an experiment, a sphere of aluminium of mass 0.20 kg is heated upto 150oC. Immediately, it is put into water of volume 150 cc at 27oC kept in a calorimeter of water equivalent to 0.025 kg. Final temperature of the system is 40oC. The…2017 · MCQ
  • N moles of a diatomic gas in a cylinder are at a temperature T. Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas get converted into monoatomic gas. What is the change in the total…2017 · MCQ
  • A steel rail of length 5 m and area of cross section 40cm2 is prevented from expanding along its length while the temperature rises by 10oC. If coefficient of linear expansion and Young’s modulus of steel are 1.2×10−5 K−1 and 2×1011 Nm−2…2017 · MCQ
  • For the P-V diagram given for an ideal gas, out of the following which one correctly represents the T-P diagram ? Includes diagram2017 · MCQ
  • CP and Cv are specific heats at constant pressure and constant volume respectively. It is observed that CP – Cv = a for hydrogen gas CP – Cv = b for nitrogen gas The correct relation between a and b is2017 · MCQ
  • The temperature of an open room of volume 30 m3 increases from 17oC to 27oC due to the sunshine. The atmospheric pressure in the room remains 1 × 105 Pa. If Ni and Nf are the number of molecules in the room before and after heating,…2017 · MCQ
  • An external pressure P is applied on a cube at 0oC so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and α is its coefficient of linear expansion. Suppose we want to bring the cube to…2017 · MCQ