8-39 A 0.8-m^3 insulated rigid tank contains 1.54 kg of carbon dioxide at 100 kPa. Now paddle-w

step 1 Hi friends, the initial and final temperature, initial and final temperature using ideal gas equ

8-39 A 0.8-m^3 insulated rigid tank contains 1.54 kg of...

$8-39$ A $0.8-\mathrm{m}^{3}$ insulated rigid tank contains $1.54 \mathrm{~kg}$ of carbon dioxide at $100 \mathrm{kPa}$. Now paddle-wheel work is done on the system until the pressure in the tank rises to $135 \mathrm{kPa}$. Determine $(a)$ the actual paddle-wheel work done during this process and $(b)$ the minimum paddle-wheel work with which this process (between the same end states) could be accomplished. Take $T_{0}=298 \mathrm{~K}$.

Key Concepts

First Law of Thermodynamics

In a closed system, the first law relates the change in internal energy to work and heat transfer. With no heat exchange in an insulated system, any work (such as paddle-wheel work) directly contributes to changing the internal energy of the system.

Closed System Analysis

A rigid tank represents a closed system where mass remains constant and the volume is fixed. This simplifies the energy balance by eliminating boundary work associated with volume change, so work and internal energy change become the focal points.

Adiabatic Process

An adiabatic process is one in which no heat is transferred to or from the system. For an insulated rigid tank, the process is inherently adiabatic, meaning that any energy added through work goes entirely into increasing the system's internal energy.

Irreversible vs. Reversible Processes

Real processes often involve irreversibilities such as friction and turbulence, causing extra work to be required compared to an ideal reversible process. The minimum work represents the theoretical work under reversible conditions, whereas the actual work is higher due to these dissipative effects.

Paddle-Wheel Work

Paddle-wheel work refers to the work input via a mechanical device that agitates the fluid, increasing its internal energy and pressure. This concept highlights the difference between the actual work done, which includes losses due to irreversibilities, and the ideal minimal work required in a reversible process.

Transcript

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