The zeroth law makes temperature a consistent comparison: two bodies that separately equilibrate with the same thermometer are at the same temperature as each other. Set both bodies to the thermometer reading to establish the relation.
The first law is an energy balance. Heat entering increases internal energy; work done by the gas decreases it. Compression has negative work-by and can raise energy even without heat.
Pressure, volume, temperature and gas amount are related by the equation of state. At fixed amount and temperature, doubling volume halves pressure. Internal energy of this ideal monatomic gas depends on temperature alone.
An isothermal gas exchanges heat to keep its temperature fixed as it expands. A reversibly adiabatic gas receives no heat, so expansion work lowers its internal energy and temperature. The adiabatic pressure falls more steeply.
Internal energy returns to its starting value over a cycle, but net work can be nonzero. The signed area inside a PV loop measures that work. A clockwise loop produces positive work; reversing it requires work input.
Conservation of energy alone permits either direction of heat transfer. The second law selects the spontaneous direction by requiring nondecreasing total entropy. Heat flows from hot to cold without external work.
A heat engine must reject some heat to the cold reservoir. The reversible Carnot efficiency depends only on absolute reservoir temperatures. Increasing their temperature separation increases the ideal efficiency.
A gas compressed without cooling becomes hotter and resists more strongly than a gas allowed to remain isothermal. Consequently its adiabatic bulk modulus is γ times its isothermal value at the same starting pressure.