to calculate the number of molecules in the gas, with some additional nformation provided. For an isothermal expansion, does the pressure of the gas remain constant? Hint for (a) No, it does not remain constant. O Yes, it remains constant. O Answer depends on additional information not given. f the pressure does not remain constant, we cannot calculate the whole amount of work with W = PAV. Instead, we need to start out with the infinitesimal work done for infinitesimal volume thange (dW = PdV) and integrate over the interval of volume change to calculate the total work one (this is also same as the area under the curve in P-V diagram). ill in the blank in the setup for the integral below, in terms of V (volume), N (number of nolecules), T (temperature), and k (Boltzmann constant) and other numerical constants. Hint for (b) otal work done in volume change from Vị to Vj is, *AP Complete the integral above and write down work done in terms of Vị, Vj, N, T, k, and other mumerical constants. Hint for (c) otal work done in volume change from V; to V; is, v =| Format hint: Subscripts are typed using underscores. For example, to type Vi, type in "V_ï". Natural ogs are represented with function "In". That is, for "natural log of 12", for example, type in "In(12)".) uppose that amount of 375 J of work was done in this expansion. Find the value of N (that is, how nany molecules are in this gas?). Hint for (d) Format Hint: Use the "E" notation to enter numbers in scientific notation. For example, 3.14 x 102 an be written as "3.14E12".)
A dilute gas expands quasi-statically from 0.3 to 5 L at a constant temperature of 280 K. Follow the steps below to calculate the number of molecules in the gas, with some additional information provided.
Hint
-
For an isothermal expansion, does the pressure of the gas remain constant?
Hint for (a)
- No, it does not remain constant.
- Yes, it remains constant.
- Answer depends on additional information not given.
-
If the pressure does not remain constant, we cannot calculate the whole amount of work with W=PΔVW=PΔV. Instead, we need to start out with the infinitesimal work done for infinitesimal volume change (dW=PdVdW=PdV) and integrate over the interval of volume change to calculate the total work done (this is also same as the area under the curve in P-V diagram).
Fill in the blank in the setup for the integral below, in terms of VV (volume), NN (number of molecules), TT (temperature), and kk (Boltzmann constant) and other numerical constants.
Hint for (b)
Total work done in volume change from ViVi to VfVf is,
W=∫VfViW=∫ViVf dVdV. -
Complete the integral above and write down work done in terms of ViVi, VfVf, NN, TT, kk, and other numerical constants.
Hint for (c)
Total work done in volume change from ViVi to VfVf is,
W=W= .
(Format hint: Subscripts are typed using underscores. For example, to type ViVi, type in "V_i". Natural logs are represented with function "ln". That is, for "natural log of 12", for example, type in "ln(12)".) -
Suppose that amount of 375 J of work was done in this expansion. Find the value of NN (that is, how many molecules are in this gas?).
Hint for (d)
N=N=.
(Format Hint: Use the "E" notation to enter numbers in scientific notation. For example, 3.14×10123.14×1012 can be written as "3.14E12".)
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