A block of ice, 150.6g is initially at 0°C. The ice is heated until it has turned to water at a temperature of 69.4°C. The specific heat of water is 4186J kg°C The latent heat of fussion for water is How much Lf = 334 kJ kg°C° heat has been added to the ice (in kJ)? (Assume ideal conditions and no heat loss).
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- A mole of ideal monatomic gas at 0 and 1.00 atm is warmed up to expand isobarically to triple its volume. How much heat is transferred during the process?By counting squares in the following figure, estimate the fraction of argon atoms at T = 300 K that have speeds between 600 m/s and 800 m/s. The curve is correctly normalized. The value of a square is its length as measured on the x-axis times its height as measured on the y-axis, with the units given on those axes. `After a free expansion to quadruple its volume, a mole of ideal diatomic gas is compressed back to its original volume isobarically and then cooled down to its original temperature. What is the minimum heat removed from the gas in the final step to restoring its state?
- Check your Understanding Show that QhQh=QcQc for the hypothetical engine of Figure 4.10 The second property to be demonstrated is that all reversible engines operating between the same two reservoirs have the same efficiency. To this, stat with the two engines D and E of Figure 4.10 (a), which are operating between two common heat reservoirs at temperatures Th and Tc . First, assume that D is a reversible engine and that E is a hypothetical irreversible engine that has a higher efficiency than D. If both engines perform the same amount of work W per cycle, it follows from Equation 4.2 that QhQh . It then follows from the first law that QcQc . Figure 4.10 (a) Two uncoupled engines D and E working between the same reservoirs. (b) The engines, With D working reverse. Suppose the cycle of D is so that it operates as a refrigerator, and the two engines are coupled such that the work output of E is used to drive D, as shown in Figure 4.10(b). Since QhQh and QcQc , the net result of each cycle is equivalent to a spontaneous transfer of heat from the cold reservoir to the hot reservoir, a process second law does not allow. The original assumption must therefore be wrong, and it is impossible to construct an irreversible engine such that E is more efficient than the reversible engine D. Now it is quite easy to demonstrate that the efficiencies of all reversible engines operating between the same reservoirs are equal. Suppose that D and E are reversible engines. If they are as shown in Figure 4.10(b), the efficiency of E cannot be greater than the efficiency of D, or second law would violated. If both engines are then reversed, the same reasoning implies that the efficiency of D cannot be greater than the efficiency of E. Combining these results leads to the conclusion that all reversible engines working between same two reservoirs have the same efficiency.The paths ABC, AC, and ADC represent three different quasi-static transitions between the equilibrium states A and C . Check Your Understanding How much work is done by gas, as given in Figure 3.6, when it expands quasi-statically along the path ADC?A car tile contains 0.0380 m3 of air at a pressure of 2.20105 Pa (about 32 psi). How much more internal energy does this gas have than the same volume has at zero gauge pressure (which is equivalent to normal atmospheric pressure)?
- Nuclear fusion, the energy solute of Sun, hydrogen bombs, and fusion reactors, occurs much more readily when the average kinetic energy of the atoms is high—that is, at high temperatures. Suppose you want the atoms in your fusion experiment to have average kinetic energies of 6.41014 J . What temperature is needed?In an adiabatic process, oxygen gas in a container is compressed along a path that can be described by the following pressure in atm as a function of volume V, with V0=1L:P=(3.0atm)(V/V)1.2 . The initial and final volumes during the process were 2 L and 1.5 L, respectively. Find the amount of work done on the gas.What does the first law of thermodynamics tell us about the energy of the universe? `
- On an adiabatic process of an ideal gas pressure, volume and temperature change such that pV is constant with =5/3 for monatomic gas such as helium and =7/5 for diatomic gas such as hydrogen at room temperature. Use numerical values to plot two isotherms of 1 mol of helium gas using ideal gas law and two adiabatic processes mediating between them. Use T1=500K,V1=1L, and T2=300K for your plot.An ideal diatomic gas at 80 K is slowly compressed adiabatically to one-third its original volume. What is its final temperature?A cylinder containing three moles of a monatomic ideal gas is heated at a constant pressure of 2 atm. The temperature of the gas changes from 300 K to 350 K as a result of the expansion. Find work done (a) on the gas; and (b) by the gas.