Question

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

Answer 1

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 C_v is the heat capacity of bomb calorimeter then q= -C_vT. Here ?U =?H.