What is the change in internal energy of the gas?

[Polo12]

1. Cylinder contains 0.1 mol of ideal gas at a pressure of 2 atm and temperature of 300 K. The volume of the cylinder is 1.25 x 10^-3 m3. When the gas is heated from 300K to 350K, what is the change in internal energy of the gas?

--->(I think the equation is Q=delta U + W but I don't know how to proceed from there.)



2. So of all the properties of waves (speed, amplitude, wavelength and frequency) which one is independent of the others?

--> Is it amplitude?

3. A train is blowing its whistle at 860Hz while traveling at a speed of 40m/s. The speed of sound is 340 m/s. What is the frequency heard by a stationary observer in front of the train?

---> I used the equation, f'= f (1/1+ or - Vs/V) and I got 769 Hz as the answer but I'd like to confirm with someone whether I am doing it correctly.


Thanks!

 

[Chi Meson]

1. the volume of the cylinder does not change so work is zero. Now you need to know how much heat is required to change the temperature of a gas at constant volume.

2. No. Which property of a wave stays the same when it enters a new medium?

3. Observer in front of the train should hear what, a higher or lower pitch?

 

[Polo12]

Thanks. I worked through the #2 and 3 and I am all set with those two. But I cannot get the first problem right.

To find heat, I used Q=nCp(deltaT)

and with W=0.

then plugged into Q=(delta U) + W.

Is there something that I am doing wrong?

 

[Chi Meson]

Hope this is not too late, but

Cp is for constant pressure. This cylinder has constant volume. Otherwise, you're fine.

 

[qtp]

how is amplitude not independant of the other three? when velocity = freq x wavelength

 

[Chi Meson]

how is amplitude not independant of the other three? when velocity = freq x wavelength

I think the intended answer is indeed amplitude.

I don't really like the original question; this how I saw it:

The wave speed is determined by the medium. If a wave transmits into a new medium, its frequency is what stays the same as the wave speed changes. As a result the wavelength changes to keep the ratio of velocity/wavelength constant.

Simultaneously, the energy of a wave is proportional to the wave speed, the frequency squared and the amplitude squared, so if the wave speed increases, the amplitude must decrease so as not to violate the Law of conservation of energy. The frequency is the only property that stays constant "independant of the other three." I think I was going too far beyond the intent of the question.