A 364 g block is put in contact with a thermal reservoir. The block is initially at a lower temperature than the reservoir. Assume that the consequent transfer of energy as heat from the reservoir to the block is reversible. Figure gives the change in entropy of the block until thermal equilibrium is reached. The scale of the horizontal axis is set by . What is the specific heat of the block?
Specific heat of the block is 450 J/kg K .
a) Mass of the block, m = 364 g or 0.364 kg
b) The graph of entropy change vs. temperature is given.
c) Temperature of horizontal axis,
Entropy change is a phenomenon that quantifies how disorder or randomness has changed in a thermodynamic system. We can write the formula for specific heat by rearranging the formula for entropy change. Then inserting the values obtained from the given graph, we can find the specific heat of the block.
The entropy change of the gas, …(i)
Using equation (i) and the given values, the specific heat of the block is given as:
(From the graph, we can infer that
Hence, the value of the specific heat of the block is
A 2.0 mol sample of an ideal monatomic gas undergoes the reversible process shown in Figure. The scale of the vertical axis is set by and the scale of the horizontal axis is set by . (a) How much energy is absorbed as heat by the gas? (b) What is the change in the internal energy of the gas? (c) How much work is done by the gas?
An inventor claims to have invented four engines, each of which operates between constant-temperature reservoirs at 400 and 300K. Data on each engine, per cycle of operation, are: engine A, , and W = 40 J; engine B, ,and W = 400 J; engine C, , and W = 400 J; engine D, , and W = 10J. Of the first and second laws of thermodynamics, which (if either) does each engine violate?
A 2.0 mol diatomic gas initially at 300 K undergoes this cycle: It is (1) heated at constant volume to 800 K , (2) then allowed to expand isothermally to its initial pressure, (3) then compressed at constant pressure to its initial state. Assuming the gas molecules neither rotate nor oscillate, find (a) the net energy transferred as heat to the gas, (b) the net work done by the gas, and (c) the efficiency of the cycle.
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