What would be the isothermal bulk modulus B_T for diatomic hydrogen gas at stand

Question

What would be the isothermal bulk modulus B_T for diatomic hydrogen gas at standard temperature and pressure (STP) if the gas were assumed to be an ideal gas? The adiabatic speed of sound in an ideal gas is related to the isothermal bulk modulus via v_sound = square root gamma B_T RT/MP where gamma is the adiabatic exponent and M is the molecular weight (kg per mole). For hydrogen gas at STP, v_sound is measured to be 1290 m/s. Assuming it is a diatomic gas, what does this imply for the value of gamma for hydrogen? How close is this to 7/5?

Explanation / Answer

isothermal bulk modulus = P at STP

http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/propsoffluids/node14.html

Pressure, P at STP is 1.01325*10^5 N/m^2

v = sqrt{ (gamma*BT*R*T) / (M*P)}

Since BT =P

v = sqrt{ (gamma*R*T) / M}
1290^2 = gamma * 8.314 * 273 / 0.002
gamma =1.47

7/5 = 1.4

so gamma = 1.47 is very close to 1.4
the deviation is just (1.47-1.4)*100 / 1.4 = 5%

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.