Question

# for the following processes, state whether each of the thermodynamics quantities, q, w, delta U, and...

for the following processes, state whether each of the thermodynamics quantities, q, w, delta U, and delta H is greater than, equal to, or less than zero for the system described. Explain your answers briefly

a) an ideal gas expands adiabaticalally against an external pressure of 1 bar.

b) an ideal gas expands isothermally against an external pressure of 1 bar

c) an ideal gas expands adiabatically into a vacuum

d) a liquid at its boiling point is converted reversibly into its vapor, at constant temperature and 1 bar pressure

e)H2 gas and O2 gas react in closed bomb at 25 degree Celsius, and the product water is brought back to 25 degree Celsius

1. When an ideal gas expands adiabatically, there is no change in heat gained or lost , therefore q=0. From the First Law of thermodynamics ?U =q-w. As q=0, therefore ?U = -w which means that the decrease in internal energy is exactly equal to the work done on the system by surrounding.

For ?H=?U+P?V as P?V = w therefore ?H = ?U+w

From the above we know that in this case ?U = -w

Therefore, ?H=-w+w =0

The pressure of 1bar is nearly equal to 1atm which is the standard pressure.

1. When an ideal gas expands isothermally, ?U= 0. First Law of thermodynamics ?U =q-w. As ?U = 0, therefore q-w =0 or q=w

For ?H=?U+P?V as ?U =0 therefore, ?H = +w. So, ?H has value greater than zero.

1. For an ideal gas expansion adiabatic ally into vaccum , work done is zero. As the process is adiabatic q = 0, as both q and w is zero therefore, ?U =0. ?H =0 also.
2. For isothermal process i.e where temperature is constant, work done is equal to PV as this process is reversible therefore w = -P ? V. Here q has value than zero. As temperature is constant ?U =0, ?H has value less than zero too.
3. Lets suppose q is the quantity of heat of released on mixing hydrogen and oxygen and Cv is the heat capacity of bomb calorimeter then q= -CvT. Here ?U =?H.

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