In a pressure cooker cooking is faster because the increase in vapour pressure :

Cooking in a pressure cooker is faster because the sealed environment traps steam, which significantly increases the internal pressure [t5][t6]. The boiling point of a liquid is the temperature at which its vapor pressure equals the surrounding atmospheric pressure [t2]. By increasing the ambient pressure inside the cooker, the water molecules require more kinetic energy to escape into the gaseous state, thereby increasing the boiling point [c5][t1]. In a standard pressure cooker, the boiling point of water rises from 100°C to approximately 121°C [t2][t5]. This higher temperature accelerates the chemical reactions involved in cooking, such as the Maillard reaction, allowing food to cook much faster than in an open vessel where the temperature is capped at the normal boiling point [t5][t10]. Specific heat is a material property and is not the primary mechanism for faster cooking in this context.

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 3: Geological Time Scale The Evolution of The Earths Surface > 3. Geological Time Scale – The Evolution of The Earth's Surface > p. 43