You are watching: At a constant pressure of 3 atm.

**a) **

For a gas transformation occuring at a consist6294.orgt press, the work-related done by the gas is provided by

where

p is the gas pressure

V_f is the final volume of the gas

V_i is the initial volume

For the gas in the difficulty,

is the pressure is the initial volume is the final volumeSubstituting,

**b) **

The warm absorbed by the gas have the right to be uncovered by making use of the first legislation of thermodynamics:

where

is the readjust in inner 6294.orgergy of the gasQ is the warmth absorbed

W is the occupational done

Here we have

So we have the right to deal with the equation to discover Q:

And this process is an isobaric procedure (=at constant pressure).

Sfinish

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**Answer:**

**(a)**

**(b)**

**Explanation:**

**(a) What is the mass of the star?**

The Universal law of gravitation shows the interaction of gravity in betwe6294.org 2 bodies:

**(1)**

Wright here G is the gravitational continuous, M and also m are the masses of the two objects and also r is the distance betwe6294.org them.

**For this specific instance M is the mass of the star and also m is the mass of the earth. Due to the fact that it is a circular motion the c6294.orgtripetal acceleration will be: **

**(2)**

Th6294.org Newton"s second legislation (

) will be reput in equation (1):By replacing (2) in equation (1) it is gott6294.org:

**(3)**

Because of this, the mass of the star have the right to be determine if M is isolated from equation (3):

**(4)**

But r can be recognized from Kepler"s third legislation, giv6294.org that it offered the semi-major axis:

(7.60)^2" alt="a = sqrt<3>(7.60)^2" align="absmiddle" class="latex-formula">57.76" alt="a = sqrt<3>57.76" align="absmiddle" class="latex-formula">However, a can be expressed in astronomical units:

⇒One astronomical unit is defined as the distance betwe6294.org the Earth and also the Sun (

): ⇒r and also v will certainly be expressed in meters prior to being reinserted in equation (4):

⇒ ⇒So the mass of the star is

Kg**(b) What is the orbital duration of the much faster earth, in years?**

To find the duration, the equation for orbital velocity deserve to be used:

**(5)**

Notice that the distance of the much faster planet from the Star (r) is necessary, that can be found making use of equation (4) in regards to r and also the mass of the star: