CT20-1 A container with a piston-lid contains an ideal gas at temperature T = 27 oC (300 K) and a volume Vo. The temperature is increased to Tf = 127 oC while the pressure is kept constant. What is the new volume?A: VoB: (127/27)VoC: (4/3) VoD: (3/4) VoE: None of these.Answer: Since P=constant (and N=constant), we have V/T=constant , VTVTVTTV Voofffofo o ,400300. You have to remember touse degrees Kelvin for temperature, always. Answer: (4/3)Vo. constant pressureCT20-2. An ideal gas in a container with a piston lid has a pressurepo=1atm, volume Vo, and temperature To = 300K. The piston lid is pushed in, reducing the volume to Vo/2. At the same time, the temperature is reduced to Tf = 150K. What is the final pressure? (Hint: pV = N k T) A: 1 atmB: 2 atmC: 4 atmD: 0.5 atmE: None of these.Answer: pV = NkT, but only N is constant; we cannot assume p, V,or T is constant. However, since both T and V decrease by a factor of 2, the equation pV=NkT remains true if p does not change. Answer is 1 atm.Or, using a little more algebra, since N=const, PVTP VTP VTPVVTTP Po oof ffooffoo o constant, Pf, ( )( / )2 1 2CT20-3. A square metal plate with edge length Lo (area A = Lo2) isheated so that it expands and its new edge length is 1.01 Lo. What is its new area?A: (1.01) Lo2 B: Less than (1.01) Lo2 C: More than (1.01) Lo2Answer: The new area is (1.01 Lo)2 = 1.02 Lo2. (1.01)2 = (1+0.01)(1.01) = 1.01 + (0.01)(1.01) 1.01 + 0.01= 1.02CT20-4. Brass has a positive coefficient ofthermal expansion (L = Lo T). A ring(annulus) of brass is heated. Does the hole inthe middle of the ring get larger or smaller?A: larger B: smaller C: stays the sameANSWER: When a two or three-dimensional object is heated it expands in every direction so that every dimension is larger.
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