Shortcut Methods
JEE:
1. For isothermal expansion:
$$\Delta U=0$$
For isochoric process from (P_1,V_1,T_1)\to(P_2,V_1,T_2):$$ $$\Delta U=C_v(T_2-T_1)$$ $$\Delta U=(3R/2)(327-27)\ \Delta U=450\ J$$
2. Heat lost by water= Heat gained by the Ice. $$Q_w+Q_i=0$$ $$m_wc_w(\Delta T_w)=-m_ic_i(\Delta T_i)+m_il_f$$ $$(1000)(4186)(T_f-100)=-(200)(2090)(327-0)+200333800$$
$$T_f=10.3\degree C$$
3. For an ideal gas $$P_1V_1/T_1=P_2V_2/T_2$$ $$T_2=P_2V_2/P_1V_1T_1$$ $$T_2=600/300=2$$ $$T_2=600\ K$$
CBSE Board:
1. According to the ideal gas equation, $$PV = nRT$$
If V decreases and T remains constant then P increases.
2. The law of conservation of energy states that the total amount of energy in an isolated system remains constant, although the form of the energy may change. An example of this law is when a ball is thrown into the air. The initial energy of the ball is in the form of kinetic energy. As the ball reaches the top of its trajectory, its kinetic energy is converted into potential energy. When the ball falls, the potential energy is converted back into kinetic energy.
3. Heat is the energy that flows from a hotter object to a colder object, while internal energy is the total energy of a system, including the kinetic energy of the particles in the system and the potential energy of the system due to the interactions of the particles.
